Question

Find the solution for the given equation

$\frac{x+y-8}{2}$ = $\frac{x+2y-14}{8}$ = $\frac{3x+y-12}{11}$

• A. (1,-1)
• B. (2,6)
• C. (2,2)
• D. (0,1)

Answer 1

The correct option is B

(2,6)

$\frac{x+y-8}{2}$ = $\frac{x+2y-14}{8}$

$\Rightarrow$ 8(x + y - 8) = 2(x + 2y - 14)
$\Rightarrow$ 3x + 2y - 18 = 0 -----------(i)

$\frac{x+2y-14}{8}$ = $\frac{3x+y-12}{11}$

$\Rightarrow$ 11(x +2 y - 14) = 8(3x + y - 12)

$\Rightarrow$ -13x + 14y - 58 = 0 -----------(ii)

Multiply (i) by 7, $\Rightarrow$ 21x + 14y - 116 = 0....(iii)

Subtract (ii) from (iii), we get

34x = 68 $\Rightarrow$ x = 2

y =6 [by substituting x=2 in (i)]