Question

Find the solution of the given system of equations.

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

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

Answer 1

The correct option is B

(2, 6)

Take first two components,

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

$\Rightarrow 8(x+y-8)=2(x+2y-14)$
$\Rightarrow 8x+8y-64=2x+4y-28$
$\Rightarrow 6x+4y-36=0$

$\Rightarrow 3x+2y-18=0.....\left(i\right)$

Take last two components,

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

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

$\Rightarrow 11x+22y-154=24x+8y-96$

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

On multiplying equation $\left(i\right)$ by 7, we get

$\Rightarrow 21x+14y-126=\mathrm{0...}\left(iii\right)$,

On subtracting equation (ii) from (iii), we get

$\Rightarrow 34x=68$

$\Rightarrow x=2$

On substituting value of $x=2$ in equation $\left(i\right)$, we get

$3\times 2+2y-18=0$

$\Rightarrow y=6$

$\therefore$ The solution is (2, 6).