Solve the question no.29 Solve the question no.29 v awe 01 K C 0.29 Solve the following pairs of equations unique solution kx -e Share with your friends Share 0 Devesh Kumar answered this Given pair of linear equations:(a-b)x +(a+b)y=a2-2ab-b2 ............[1](a+b)x +(a+b)y=a2+b2 ....................[2][1], [2] can be written as:ax-bx+ay+by=a2-2ab-b2 .............[3]ax+bx+ay+by=a2+b2........................[4]Now subtract [4] from [3] ax-bx+ay+by= a2-2ab-b2 ax+bx+ay+by= a2 +b2 - - - - - - 0-2bx+0+0= -2ab-2b2 now, -2bx=-2ab-2b2 ⇒ -2bx=-2b(a+b) ⇒ x=a+bNow for the value of y, by using elimination method, Multiply [1] by (a+b) and [2] by (a-b) both sides.eqn [1] will become(a+b)(a-b)x +(a+b)2 y=(a2-2ab-b2) (a+b)⇒(a+b)(a-b)x +(a+b)2 y=a3-2a2b-b2a+a2b-2ab2-b3⇒(a+b)(a-b)x +a2y+b2y+2aby=a3-b3-a2b-3ab2 .......................[5]eqn [2] will become(a+b)(a-b)x +(a-b)(a+b)y=(a2+b2)(a-b)⇒(a+b)(a-b)x+a2y-b2y=a3-b3-a2b+ab2 ...........................[6]Now subtract [6] from [5] (a+b)(a-b)x +a2y+b2y+2aby= a3-b3-a2b-3ab2 (a+b)(a-b)x+a2y-b2y = a3-b3-a2b+ab2 - - + - + + - 0+0 +2b2y+2aby= 0 +0+0-4ab2 Now 2b2y+2aby=-4ab2 ⇒2b(b+a)y=-4ab2 ⇒(b+a)y=-2ab ⇒y=-2ab b+a 3 View Full Answer
