Question

Solve the following pair of linear equations by the substitution method.

$\frac{3x}{2}-\frac{5y}{3}=-2,\frac{x}{3}+\frac{y}{2}=\frac{13}{6}$

• A. $x=3,y=3$
• B. $x=1,y=3$
• C. $x=2,y=3$
• D. $x=0,y=0$

Answer 1

Answer: (C)

$x=2,y=3$

Given Pair of equations are:
$\frac{3x}{2}-\frac{5y}{3}=-2\Rightarrow 9x-10y=-12$ ...eq(i)
$\frac{x}{3}+\frac{y}{2}=\frac{13}{6}\Rightarrow 2x+3y=13$ ...eq(ii)
Now from eq2 will get
$2x+3y=13$
Now using substitution method
$y=\frac{13-2x}{3}$
Now substituting y in eq (i) will get
$\Rightarrow 9x-\frac{10(13-2x)}{3}=-12$
$\Rightarrow 27x-130+20x=-36$
$\Rightarrow 47x=-36+130$
$\Rightarrow 47x=94$
$\Rightarrow x=2$
Now substituting x in eq (ii) will get
$\Rightarrow 2\times 2+3y=13$
$\Rightarrow 4+3y=13$
$\Rightarrow 3y=13-4$
$\Rightarrow 3y=9$
$\Rightarrow y=3$
$\Rightarrow x=2,y=3$