NCERT Solutions for Class 9 Maths in Hindi Medium<\/a>. Here we have given NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables.<\/p>\n\u092a\u094d\u0930\u0928\u093e\u0935\u093e\u0932\u0940 4.1<\/strong><\/span><\/p>\nEx 4.1 Class 9 \u0917\u0923\u093f\u0924 Q1. <\/strong>\u090f\u0915 \u0928\u094b\u091f\u092c\u0941\u0915 \u0915\u0940 \u0915\u0940\u092e\u0924 \u090f\u0915 \u0915\u0932\u092e \u0915\u0940 \u0915\u0940\u092e\u0924 \u0938\u0947 \u0926\u094b \u0917\u0941\u0928\u0940 \u0939\u0948\u0964 \u0907\u0938 \u0915\u0925\u0928 \u0915\u094b \u0928\u093f\u0930\u0942\u092a\u093f\u0924 \u0915\u0930\u0928\u0947<\/strong>\u00a0\u0915\u0947 \u0932\u093f\u090f \u0926\u094b \u091a\u0930\u094b\u0902 \u0935\u093e\u0932\u093e \u090f\u0915 \u0930\u0948\u0916\u093f\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u0932\u093f\u0916\u093f\u090f\u0964\u00a0<\/strong>(<\/strong>\u0938\u0902\u0915\u0947\u0924<\/strong>\u00a0\u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f<\/strong>,\u00a0<\/strong>\u0928\u094b\u091f\u092c\u0941\u0915 \u0915\u0940 \u0915\u0940\u092e\u0924 x \u0930\u0941 \u0939\u0948 \u0914\u0930 \u0915\u0932\u092e \u0915\u0940 \u0915\u0940\u092e\u0924 y \u0930\u0941 \u0939\u0948)\u0964<\/strong>
\n\u0939\u0932 :<\/strong>
\n\u092e\u093e\u0928\u093e \u092a\u0947\u0928 \u0915\u0940 \u0915\u0940\u092e\u0924 \u00a0= y \u0930\u0941\u092a\u092f\u093e \u0939\u0948
\n\u0914\u0930 \u0928\u094b\u091f\u092c\u0941\u0915 \u0915\u0940 \u0915\u0940\u092e\u0924 = x \u0930\u0941\u092a\u092f\u093e \u0939\u0948
\n\u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0928\u0941\u0938\u093e\u0930,
\n\u0928\u094b\u091f\u092c\u0941\u0915 \u0915\u0940 \u0915\u0940\u092e\u0924 = 2 ( \u092a\u0947\u0928 \u0915\u0940 \u0915\u0940\u092e\u0924 )
\nx = 2y
\n\u21d2 x – 2y = 0<\/p>\nEx 4.1 Class 9 \u0917\u0923\u093f\u0924\u00a0Q2. \u00a0\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0930\u0948\u0916\u093f\u0915 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u094b\u00a0ax\u00a0+\u00a0by\u00a0+\u00a0c\u00a0= 0 \u00a0\u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u0940\u091c\u093f\u090f \u0914\u0930 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0938\u094d\u0925\u093f\u0924\u093f \u092e\u0947\u0902 \u00a0a,\u00a0b \u0914\u0930\u00a0c \u0915\u0947 \u092e\u093e\u0928 \u092c\u0924\u093e\u0907\u090f :<\/strong>
\n(i) 2x\u00a0<\/em>+ 3y\u00a0<\/em>= 9.35<\/strong>
\n(ii)\u00a0x\u00a0<\/em>\u2013 5y\u00a0<\/em>\u2013 10 = 0<\/strong>
\n(iii) \u20132x\u00a0<\/em>+ 3y\u00a0<\/em>= 6<\/strong>
\n(iv)\u00a0x\u00a0<\/em>= 3y<\/em><\/strong>
\n(v) 2x\u00a0<\/em>= \u20135y<\/em><\/strong>
\n(vi) 3x\u00a0<\/em>+ 2 = 0<\/strong>
\n(vii) y\u2013 2 = 0<\/strong>
\n(viii) 5 = 2x<\/em><\/strong>
\n\u0939\u0932:<\/strong>
\n(i)\u00a0 2x\u00a0<\/em>+ 3y\u00a0<\/em>= 9.35<\/strong>
\n\u0926\u093f\u090f \u0917\u090f \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u094b\u00a0ax\u00a0+\u00a0by\u00a0+\u00a0c\u00a0= 0 \u00a0\u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u0930\u0928\u0947 \u092a\u0930
\n\u21d2 \u00a02x + 3y – 9.35 = \u00a00
\n\u0905\u0924: \u00a0\u00a0a = 2, b = 3, c = – 9.35<\/p>\n\u0939\u0932:\u00a0(ii)\u00a0\u00a0x\u00a0<\/em>\u20135y<\/em>\u00a0\u2013 10 = 0<\/strong>
\n\u0926\u093f\u090f \u0917\u090f \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u094b\u00a0ax\u00a0<\/em>+\u00a0by\u00a0<\/em>+\u00a0c\u00a0<\/em>= 0 \u00a0\u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u0930\u0928\u0947 \u092a\u0930
\n\u21d2\u00a0x\u00a0<\/em>\u20135y<\/em>\u00a0\u2013 10 = 0
\n\u0905\u0924: , a = 1, b = -5, c = -10<\/p>\n\u0939\u0932:\u00a0(iii)\u00a0 \u20132x\u00a0<\/em>+ 3y\u00a0<\/em>= 6<\/strong>
\n\u0926\u093f\u090f \u0917\u090f \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u094b\u00a0ax\u00a0<\/em>+\u00a0by\u00a0<\/em>+\u00a0c\u00a0<\/em>= 0 \u00a0\u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u0930\u0928\u0947 \u092a\u0930
\n\u21d2 \u20132x\u00a0<\/em>+ 3y<\/em>\u00a0\u2013 6 = 0
\n\u0905\u0924:, a = \u2013 2, b = 3, c = \u2013 6<\/p>\n\u0939\u0932:\u00a0(iv)\u00a0\u00a0x\u00a0<\/em>= 3y<\/em><\/strong>
\n\u0926\u093f\u090f \u0917\u090f \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u094b\u00a0ax\u00a0<\/em>+\u00a0by\u00a0<\/em>+\u00a0c\u00a0<\/em>= 0 \u00a0\u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u0930\u0928\u0947 \u092a\u0930
\n\u21d2\u00a0x<\/em>\u00a0–<\/em>\u00a03y<\/em>\u00a0=<\/em>\u00a0\u00a00<\/em>
\n\u0905\u0924:<\/em>, a<\/em>\u00a0= 1, b<\/em>\u00a0=\u00a0<\/em>\u20133, c= 0<\/em><\/p>\n\u0939\u0932:\u00a0(v)\u00a0 2x\u00a0<\/em>= \u20135y<\/em><\/strong>
\n\u0926\u093f\u090f \u0917\u090f \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u094b\u00a0ax\u00a0<\/em>+\u00a0by\u00a0<\/em>+\u00a0c\u00a0<\/em>= 0 \u00a0\u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u0930\u0928\u0947 \u092a\u0930
\n\u21d2\u00a02x<\/em>\u00a0+<\/em>\u00a05y<\/em>\u00a0= 0<\/em>
\n\u0905\u0924:<\/em>, a<\/em>\u00a0= 2, b<\/em>\u00a0= 5, c<\/em>\u00a0= 0<\/em><\/p>\n\u0939\u0932:\u00a0(vi)\u00a0 3x\u00a0<\/em>+ 2 = 0<\/strong>
\n\u0926\u093f\u090f \u0917\u090f \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u094b\u00a0ax\u00a0<\/em>+\u00a0by\u00a0<\/em>+\u00a0c\u00a0<\/em>= 0 \u00a0\u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u0930\u0928\u0947 \u092a\u0930
\n\u21d2 3x + 0.y + 2 = 0
\n\u0905\u0924:<\/em>, a = 3, b = 0, c = 2<\/p>\n\u0939\u0932:\u00a0(vii)\u00a0\u00a0y\u00a0<\/em>\u2013 2 = 0<\/strong>
\n\u0926\u093f\u090f \u0917\u090f \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u094b\u00a0ax\u00a0<\/em>+\u00a0by\u00a0<\/em>+\u00a0c\u00a0<\/em>= 0 \u00a0\u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u0930\u0928\u0947 \u092a\u0930
\n\u21d2\u00a00.x + y\u00a0<\/em>\u2013 2 = 0
\n\u0905\u0924:, a = 0, b = 1, c = -2<\/p>\n\u0939\u0932:\u00a0(Viii)\u00a0 5 = 2x<\/em><\/strong>
\n\u0926\u093f\u090f \u0917\u090f \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u094b\u00a0ax\u00a0<\/em>+\u00a0by\u00a0<\/em>+\u00a0c\u00a0<\/em>= 0 \u00a0\u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u0930\u0928\u0947 \u092a\u0930
\n\u21d22x – 5= 0
\n\u0905\u0924:, a\u00a0= 2, b\u00a0= 0, c\u00a0= -5<\/p>\n\u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 4.2<\/strong><\/span><\/p>\nEx 4.2 Class 9 \u0917\u0923\u093f\u0924 Q1. \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0935\u093f\u0915\u0932\u094d\u092a\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u0915\u094c\u0928-\u0938\u093e \u0935\u093f\u0915\u0932\u094d\u092a \u0938\u0924\u094d\u092f \u0939\u0948, \u0914\u0930 \u0915\u094d\u092f\u094b\u0902?<\/strong>
\ny\u00a0<\/em>= 3x\u00a0<\/em>+ 5 \u0915\u093e<\/strong>
\n(i) \u090f\u0915 \u0905\u0926\u094d\u0935\u093f\u0924\u0940\u092f \u0939\u0932 \u0939\u0948, \u00a0\u00a0<\/strong>
\n(ii) \u0915\u0947\u0935\u0932 \u0926\u094b \u0939\u0932 \u0939\u0948,\u00a0<\/strong>
\n(iii) \u00a0\u0905\u092a\u0930\u093f\u092e\u093f\u0924 \u0930\u0942\u092a \u0938\u0947 \u0905\u0928\u0947\u0915 \u0939\u0932 \u0939\u0948\u0902 |<\/strong>
\n\u0939\u0932 :<\/strong>\u00a0(iii) \u0905\u092a\u0930\u093f\u092e\u093f\u0924 \u0930\u0942\u092a \u0938\u0947 \u0905\u0928\u0947\u0915 \u0939\u0932 \u0939\u0948\u0902 |<\/p>\nEx 4.2 Class 9 \u0917\u0923\u093f\u0924\u00a0Q2. \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0947 \u091a\u093e\u0930 \u0939\u0932 \u0932\u093f\u0916\u093f\u090f :<\/strong>
\n(i) 2x + y = 7
\n(ii) \u03c0x + y = 9
\n(iii) x = 4y
\n
\n\u0905\u0924: x \u0914\u0930 y \u0915\u093e \u0926\u093f\u090f \u0917\u090f \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f \u091a\u093e\u0930 \u0939\u0932 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0939\u0948 :
\n
\n
\n\u0905\u0924: x \u0914\u0930 y \u0915\u093e \u0926\u093f\u090f \u0917\u090f \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f \u091a\u093e\u0930 \u0939\u0932 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0939\u0948 :
\n
\n
\n\u0905\u0924: x \u0914\u0930 y \u0915\u093e \u0926\u093f\u090f \u0917\u090f \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f \u091a\u093e\u0930 \u0939\u0932 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0939\u0948 :
\n<\/p>\nEx 4.2 Class 9 \u0917\u0923\u093f\u0924\u00a0Q3. \u092c\u0924\u093e\u0907\u090f \u0915\u093f \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0939\u0932\u094b\u0902 \u092e\u0947\u0902 \u0915\u094c\u0928-\u0915\u094c\u0928 \u0938\u092e\u0940\u0915\u0930\u0923\u00a0x\u00a0<\/em>\u2013 2y\u00a0<\/em>= 4 \u0915\u0947 \u0939\u0932 \u0939\u0948 \u0914\u0930 \u0915\u094c\u0928-\u0915\u094c\u0928 \u0928\u0939\u0940\u0902 \u0939\u0948 :<\/strong>
\n(i) (0, 2)
\n(ii) (2, 0)
\n(iii) (4, 0)
\n
\n(i) (0,2) \u0938\u092e\u0940\u0915\u0930\u0923\u00a0<\/strong>x\u00a0<\/em><\/strong>\u2013 2y\u00a0<\/em>= 4\u00a0<\/strong>\u0915\u093e \u0939\u0932 \u0939\u0948 \u0905\u0925\u0935\u093e \u0928\u0939\u0940\u0902\u00a0<\/strong>
\n\u0939\u0932<\/strong>\u00a0:<\/strong>\u00a0x = 0 \u0914\u0930 y = 2 \u0930\u0916\u0928\u0947 \u092a\u0930
\nx\u00a0<\/em>\u2013 2y\u00a0<\/em>= 4
\nLHS = 0 \u2013 2(2)
\n= – 4
\nRHS = 4
\n\u0907\u0938\u0932\u093f\u090f, LHS \u2260 RHS
\n\u0905\u0924: (0, 2) \u0926\u093f\u090f \u0917\u090f \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u093e \u0939\u0932 \u0928\u0939\u0940\u0902 \u0939\u0948 |<\/p>\n(ii) (2,0) \u0938\u092e\u0940\u0915\u0930\u0923 x \u2013 2y = 4 \u0915\u093e \u0939\u0932 \u0939\u0948 \u0905\u0925\u0935\u093e \u0928\u0939\u0940\u0902<\/strong>
\n\u0939\u0932 :<\/strong>\u00a0x \u2013 2y = 4 \u00a0\u092e\u0947\u0902\u00a0<\/strong>x = 2 \u0914\u0930 y = 0 \u0930\u0916\u0928\u0947 \u092a\u0930
\nLHS =\u00a0 2 \u2013 2(0)
\n= 2 \u2013 0
\n= 2
\n\u091c\u092c\u0915\u093f RHS = 4 \u0939\u0948
\n\u0907\u0938\u0932\u093f\u090f, LHS \u2260 RHS
\n\u0905\u0924: (2, 0) \u0926\u093f\u090f \u0917\u090f \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u093e \u0939\u0932 \u0928\u0939\u0940\u0902 \u0939\u0948 |<\/p>\n(iii) (4,0)<\/strong>\u00a0\u0938\u092e\u0940\u0915\u0930\u0923 x \u2013 2y = 4 \u0915\u093e \u0939\u0932 \u0939\u0948 \u0905\u0925\u0935\u093e \u0928\u0939\u0940\u0902<\/strong>
\n\u0939\u0932 :<\/strong>\u00a0\u0938\u092e\u0940\u0915\u0930\u0923 x \u2013 2y = 4 \u092e\u0947\u0902 x = 4 \u0914\u0930 y = 0 \u0930\u0916\u0928\u0947 \u092a\u0930
\nLHS = x \u2013 2y
\n=\u00a0 4 – 2(0)
\n=\u00a0 4 \u2013 0 = 4
\n\u091c\u092c\u0915\u093f RHS = 4
\n\u092f\u0939\u093e\u0901 LHS = RHS \u0939\u0948
\n\u0905\u0924: (4, 0) \u0926\u093f\u090f \u0917\u090f \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u093e \u0939\u0932 \u0939\u0948 |
\n<\/p>\n(v) \u092c\u0924\u093e\u0907\u090f (1,1)<\/strong>\u00a0\u0938\u092e\u0940\u0915\u0930\u0923 x \u2013 2y = 4 \u0915\u093e \u0939\u0932 \u0939\u0948 \u0905\u0925\u0935\u093e \u0928\u0939\u0940\u0902<\/strong>
\n\u0939\u0932 :<\/strong>\u00a0\u0938\u092e\u0940\u0915\u0930\u0923 x \u2013 2y = 4 \u092e\u0947\u0902 x = 1 \u0914\u0930 y = 1 \u0930\u0916\u0928\u0947 \u092a\u0930
\nLHS = x \u2013 2y = 1- 2 (1) = 1 \u2013 2 = – 1
\n\u091c\u092c\u0915\u093f RHS = 4 \u0939\u0948
\n\u0905\u0924: (1, 1) \u0938\u092e\u0940\u0915\u0930\u0923 x \u2013 2y = 4 \u0915\u093e \u0939\u0932 \u0928\u0939\u0940\u0902 \u0939\u0948 |<\/p>\nEx 4.2 Class 9 \u0917\u0923\u093f\u0924\u00a0Q4<\/strong>. k<\/strong>\u00a0\u0915\u093e \u092e\u093e\u0928 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f \u091c\u092c\u0915\u093f\u00a0<\/strong>\u00a0x\u00a0<\/strong>= 2,<\/strong>\u00a0\u00a0y\u00a0= 1\u00a0<\/strong>\u0938\u092e\u0940\u0915\u0930\u0923\u00a02x\u00a0+ 3y\u00a0=\u00a0k<\/em><\/strong>\u00a0\u0915\u093e \u090f\u0915 \u0939\u0932 \u0939\u094b |<\/strong>
\n\u0939\u0932<\/strong>\u00a0:<\/strong>\u00a02x + 3y = k
\nx = 2 \u0914\u0930 y = 1 \u0930\u0916\u0928\u0947 \u092a\u0930
\n\u21d2\u00a02x + 3y = k
\n\u21d2\u00a02(2) + 3(1) = k
\n\u21d2\u00a04 + 3 = k
\n\u21d2\u00a0k = 7<\/p>\n\u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940<\/strong>\u00a04.3<\/strong><\/span><\/p>\nEx 4.3 Class 9 \u0917\u0923\u093f\u0924 Q<\/strong>1.\u00a0<\/strong>\u0926\u094b \u091a\u0930\u094b\u0902 \u0935\u093e\u0932\u0947 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0930\u0948\u0916\u093f\u0915 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0915\u093e \u0906\u0932\u0947\u0916 \u0916\u0940\u0902\u091a\u093f\u090f :<\/strong>
\n(i)\u00a0 x\u00a0+\u00a0y\u00a0= 4
\n(ii) x\u00a0\u2013\u00a0y\u00a0= 2
\n(iii) y\u00a0= 3x
\n(iv) 3 = 2x\u00a0+\u00a0y
\n\u0939\u0932 :<\/strong>\u00a0(i) x<\/strong>\u00a0+<\/strong>\u00a0y<\/strong>\u00a0=\u00a0<\/strong>4<\/strong>
\n\u21d2 y = 4 \u2013 x
\nx \u0915\u093e \u092e\u093e\u0928 \u0915\u094d\u0930\u092e\u0936: 0, 1, \u0924\u0925\u093e 2 \u0930\u0916\u0928\u0947 \u092a\u0930 y \u0915\u093e \u092e\u093e\u0928 \u0915\u094d\u0930\u092e\u0936: 4, 3 \u0914\u0930 2 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u093f\u0938\u0915\u0940 \u0938\u093e\u0930\u0923\u0940 \u0928\u093f\u092e\u094d\u0928 \u0939\u0948 |
\n
\n
\n\u0939\u0932 :<\/strong>\u00a0(ii)\u00a0<\/strong>\u00a0\u00a0\u00a0x\u00a0<\/em><\/strong>\u2013\u00a0y\u00a0<\/em>= 2<\/strong>
\n\u21d2\u00a0x\u00a0<\/em>= 2 +\u00a0y<\/em>
\n\u0938\u092e\u0940\u0915\u0930\u0923 \u092e\u0947\u0902 y \u0915\u093e \u092e\u093e\u0928 1, 2 \u0914\u0930 3 \u0930\u0916\u0928\u0947 \u092a\u0930 y \u0915\u093e \u092e\u093e\u0928 \u0915\u094d\u0930\u092e\u0936: 3, 4 \u0914\u0930 5 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u093f\u0938\u0915\u0940 \u0938\u093e\u0930\u0923\u0940 \u0928\u093f\u092e\u094d\u0928 \u0939\u0948 –
\n
\n\u0939\u0932 :<\/strong>\u00a0(iii)\u00a0<\/strong>\u00a0\u00a0y\u00a0<\/em><\/strong>= 3x<\/em><\/strong>
\n\u0938\u092e\u0940\u0915\u0930\u0923 \u092e\u0947\u0902 x \u0915\u093e \u092e\u093e\u0928 0, 1 \u0914\u0930 \u2013 1 \u0930\u0916\u0928\u0947 \u092a\u0930 \u0915\u094d\u0930\u092e\u0936 y \u0915\u093e \u092e\u093e\u0928 0, 3 \u0914\u0930 -3 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 –
\n
\n\u0939\u0932 :<\/strong>\u00a0(iv)\u00a0<\/strong>\u00a0\u00a03 = 2x\u00a0<\/em>+\u00a0y<\/em><\/strong>
\n\u21d2\u00a0y = 3 \u2013 2x
\n\u0938\u092e\u0940\u0915\u0930\u0923 \u092e\u0947\u0902 x \u0915\u093e \u092e\u093e\u0928 0, 1 \u0914\u0930 -1 \u0930\u0916\u0928\u0947 \u092a\u0930 y \u0915\u093e \u092e\u093e\u0928 \u0915\u094d\u0930\u092e\u0936: 3, 1 \u0914\u0930\u00a0 5 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u093f\u0938\u0915\u0940 \u0938\u093e\u0930\u0923\u0940 \u0928\u093f\u092e\u094d\u0928 \u0939\u0948 –
\n<\/p>\nEx 4.3 Class 9 \u0917\u0923\u093f\u0924\u00a0Q<\/strong>2.\u00a0<\/strong>\u092c\u093f\u0902\u0926\u0941 (2, 14) \u0938\u0947 \u0939\u094b\u0915\u0930 \u091c\u093e\u0928\u0947 \u0935\u093e\u0932\u0940 \u0926\u094b \u0930\u0947\u0916\u093e\u0913\u0902 \u0915\u0947 \u0938\u092e\u0940\u0915\u0930\u0923 \u0932\u093f\u0916\u093f\u090f | \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0940 \u0914\u0930 \u0915\u093f\u0924\u0928\u0940 \u0930\u0947\u0916\u093e\u090f\u0901 \u0939\u094b \u0938\u0915\u0924\u0940 \u0939\u0948 , \u0914\u0930 \u0915\u094d\u092f\u094b\u0902 ?<\/strong>
\n\u0939\u0932 :<\/strong>\u00a0\u00a0\u00a0\u092c\u093f\u0902\u0926\u0941 (2, 14) \u092e\u0947\u0902 x = 2 \u0914\u0930 y = 14 \u0939\u0948
\n\u0905\u0924: \u0907\u0938 \u092e\u093e\u0928 \u0915\u094b \u0938\u0902\u0924\u0941\u0937\u094d\u091f \u0915\u0930\u0928\u0947 \u0935\u093e\u0932\u0947 \u0926\u094b \u0938\u092e\u0940\u0915\u0930\u0923 \u0928\u093f\u092e\u094d\u0928 \u0939\u0948 :
\nx + y = 16
\n\u0914\u0930 \u00a0x \u2013 y = \u00a0-12
\n\u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0940 \u0905\u0928\u0902\u0924 \u0930\u0947\u0916\u093e\u090f \u0939\u094b \u0938\u0915\u0924\u0940 \u0939\u0948 \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u092f\u0947 \u0930\u0947\u0916\u093e\u090f\u0901 \u090f\u0915 \u0939\u0940 \u092c\u093f\u0902\u0926\u0941 (2, 14) \u0938\u0947 \u0917\u0941\u091c\u0930\u0947\u0902\u0917\u0940 |<\/p>\nEx 4.3 Class 9 \u0917\u0923\u093f\u0924\u00a0Q<\/strong>3.\u00a0<\/strong>\u092f\u0926\u093f \u092c\u093f\u0902\u0926\u0941 (3, 4) \u0938\u092e\u0940\u0915\u0930\u0923\u00a0<\/strong>3y\u00a0<\/em>=\u00a0ax\u00a0<\/em>+ 7<\/strong>\u00a0\u0915\u0947 \u0906\u0932\u0947\u0916 \u092a\u0930 \u0938\u094d\u0925\u093f\u0924 \u0939\u0948, \u0924\u094b a \u0915\u093e \u092e\u093e\u0928 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f |<\/strong>
\n\u0939\u0932 :\u00a0<\/strong>\u00a0 3y = ax + 7
\n\u092c\u093f\u0902\u0926\u0941 (3, 4) \u092e\u0947\u0902 x = 3 \u0914\u0930 y = 4 \u0939\u0948 |
\n\u0938\u092e\u0940\u0915\u0930\u0923 3y = ax + 7\u00a0 \u092e\u0947\u0902 x \u0914\u0930 y \u0915\u093e \u092e\u093e\u0928 \u0930\u0916\u0928\u0947 \u092a\u0930
\n3(4) = a(3) +7
\n12 = 3a + 7
\n3a = 12 \u2013 7
\n3a = 5<\/p>\nEx 4.3 Class 9 \u0917\u0923\u093f\u0924\u00a0Q4.\u00a0<\/strong>\u090f\u0915 \u0928\u0917\u0930 \u092e\u0947\u0902 \u091f\u0948\u0915\u094d\u0938\u0940 \u0915\u093e \u0915\u093f\u0930\u093e\u092f\u093e \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0939\u0948: \u092a\u0939\u0932\u0947 \u0915\u093f\u0932\u094b\u092e\u0940\u091f\u0930 \u0915\u093e \u0915\u093f\u0930\u093e\u092f\u093e\u00a0<\/strong>8<\/strong>\u00a0\u0930\u0941 \u0939\u0948 \u0914\u0930 \u0909\u0938\u0915\u0947 \u092c\u093e\u0926 \u0915\u0940 \u0926\u0942\u0930\u0940 \u0915\u0947 \u0932\u093f\u090f \u092a\u094d\u0930\u0924\u093f \u0915\u093f\u0932\u094b\u092e\u0940\u091f\u0930 \u0915\u093e \u0915\u093f\u0930\u093e\u092f\u093e\u00a0<\/strong>5<\/strong>\u00a0\u0930\u0941 \u0939\u0948\u0964 \u092f\u0926\u093f \u0924\u092f \u0915\u0940 \u0917\u0908 \u0926\u0942\u0930\u0940<\/strong>\u00a0x \u0915\u093f\u0932\u094b\u092e\u0940\u091f\u0930 \u0939\u094b<\/strong>,\u00a0<\/strong>\u0914\u0930 \u0915\u0941\u0932 \u0915\u093f\u0930\u093e\u092f\u093e y \u0930\u0941 \u0939\u094b<\/strong>,\u00a0<\/strong>\u0924\u094b \u0907\u0938\u0915\u093e \u090f\u0915 \u0930\u0948\u0916\u093f\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u0932\u093f\u0916\u093f\u090f \u0914\u0930<\/strong>\u0909\u0938\u0915\u093e \u0906\u0932\u0947\u0916 \u0916\u0940\u0902\u091a\u093f\u090f\u0964<\/strong>
\n\u0939\u0932 :\u00a0<\/strong>\u00a0\u0924\u092f \u0915\u0940 \u0917\u0908 \u0926\u0941\u0930\u0940 = x km
\n\u0915\u0941\u0932 \u0915\u093f\u0930\u093e\u092f\u093e = y\u00a0 \u0930\u0941
\n\u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0928\u0941\u0938\u093e\u0930,
\n\u092a\u0939\u0932\u0947 \u0915\u093f\u0932\u094b\u092e\u0940\u091f\u0930 \u0915\u093e \u0915\u093f\u0930\u093e\u092f\u093e + 5(\u0924\u092f \u0915\u0940 \u0917\u0908 \u0926\u0941\u0930\u0940 – 1) = y
\n8 + 5(x – 1) = y
\n\u21d2\u00a08 + 5x – 5 = y
\n\u21d2\u00a03 + 5x = y
\n\u21d2\u00a05x \u2013y + 3 = 0
\n\u21d2\u00a0y = 5x + 3
\n\u0938\u092e\u0940\u0915\u0930\u0923 \u092e\u0947\u0902 x \u0915\u093e \u092e\u093e\u0928 0, -1 \u0924\u0925\u093e 1 \u0930\u0916\u0928\u0947 \u092a\u0930 y \u0915\u093e \u092e\u093e\u0928 \u0915\u094d\u0930\u092e\u0936: 3, -2 \u0914\u0930 8 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 |
\n<\/p>\nEx 4.3 Class 9 \u0917\u0923\u093f\u0924\u00a0Q<\/strong>5.\u00a0<\/strong>\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0906\u0932\u0947\u0916\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0915\u0947 \u0932\u093f\u090f \u0926\u093f\u090f \u0917\u090f \u0935\u093f\u0915\u0932\u094d\u092a\u094b\u0902 \u0938\u0947 \u0938\u0939\u0940 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u093e \u091a\u092f\u0928 \u0915\u0940\u091c\u093f\u090f:\u00a0<\/strong><\/p>\n\n\n\n\u0906\u0915\u0943\u0924\u093f 4. 6\u00a0 \u0915\u0947 \u0932\u093f\u090f<\/strong><\/td>\n\u0906\u0915\u0943\u0924\u093f 4.7 \u0915\u0947 \u0932\u093f\u090f\u00a0<\/strong><\/td>\n<\/tr>\n\n(i) \u00a0\u00a0y\u00a0<\/em>=\u00a0x<\/em> \n(ii) \u00a0x\u00a0<\/em>+\u00a0y\u00a0<\/em>= 0 \n(iii) \u00a0y\u00a0<\/em>= 2x<\/em> \n(iv) \u00a02 + 3y\u00a0<\/em>= 7x<\/em><\/td>\n(i)\u00a0y\u00a0<\/em>=\u00a0x\u00a0<\/em>+ 2 \n(ii)\u00a0y\u00a0<\/em>=\u00a0x\u00a0<\/em>\u2013 2 \n(iii)\u00a0y\u00a0<\/em>= \u2013x\u00a0<\/em>+ 2 | | | |