Question

Solve the following pairs of equations:

$\frac{x+1}{4}=\frac{2}{3}(1-2y)$
$\frac{2+5y}{3}=\frac{x}{7}-2$

• A. $x=8,y=-1$
• B. $x=3,y=-1$
• C. $x=7,y=-1$
• D. $x=9,y=-1$

Answer 1

The correct option is C $x=7,y=-1$

Given, $\frac{x+1}{4}=\frac{2}{3}(1-2y)$

$\Rightarrow 3(x+1)=8(1-2y)$

$\Rightarrow 3x+3=8-16y$

$\Rightarrow 3x+16y=5$ ....(1)

and $\frac{2+5y}{3}=\frac{x}{7}-2$

$\Rightarrow 7(2+5y)=3(x-14)$

$\Rightarrow 14+35y=3x-42$

$\Rightarrow 3x-35y=56$ ....(2)

Subtract equations (1) and (2), we get

$51y=-51$

$\Rightarrow y=-1$

Put this value in equation (1), we get

$3x+16(-1)=5$

$\Rightarrow 3x-16=5$

$\Rightarrow x=7$

Therefore, the solution is $x=7,y=-1$.