Question

Solve each system by elimination

10x-8y=4
-5x+3y=-9

Answer 1

`10x-8y =4~~~....(i)\\\\-5x+3y=-9~~~...(ii)\\\\\text{Multiply equation (ii) by} -2\\\\10x-6y = 18~~~...(iii)\\\\(iii)-(i):\\\\10x-6y - 10x +8y = 18 -4\\\\\implies 2y = 14\\\\\implies y= \frac{14}2 = 7\\\\\text{Substitute y = 7 in equation (i):}\\\\10x-8(7) =4\\\\\implies 10x - 56 =4\\\\\implies 10x = 4+56\\\\\implies 10x = 60\\\\\implies x = (60)/(10) = 6\\\\\\\text{Hence (x,y) = (6, 7)}`