Question

$\frac{x+y-8}{2}$ = $\frac{x+2y-14}{8}$ = $\frac{3x+y-12}{11}$
Solve the given system of equations:

• 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)

$\frac{x+2y-14}{8}$ = $\frac{3x+y-12}{11}$
$\Rightarrow 11(x+2y-14)=8(3x+y-12)$
$\Rightarrow -13x+14y-58=0$ -----------(ii)

Multiply (i) by 7

$21x+14y-126=0$

then subtract from (ii)

$\Rightarrow -13x+14y-58-21x-14y+126=0$
$\Rightarrow -13x-58-21x+126=0$
$\Rightarrow -34x+68=0$
$\Rightarrow x=2$

By substituting $x=2$ in (i), we get

$\Rightarrow 6+2y-18=0$
$\Rightarrow 2y-12=0$
$\Rightarrow y=6$