Question

Solve the following pair of the liner equations

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

$\frac{x}{3}+\frac{y}{2}=\frac{13}{2}$

Answer 1

Given equations are $\frac{3x}{2}-\frac{5y}{3}=-2$ and $\frac{x}{3}+\frac{y}{2}=\frac{13}{2}$

Lets take $\frac{3x}{2}-\frac{5y}{3}=-2$

$\Rightarrow \frac{9x-10y}{6}=-2$

$\Rightarrow 9x-10y=-12$ ---(1)

Now, lets take, $\frac{x}{3}+\frac{y}{2}=\frac{13}{2}$

$\Rightarrow \frac{2x+3y}{6}=\frac{13}{2}$

$\Rightarrow 2x+3y=\frac{13}{2}\times 6$

$\Rightarrow 2x+3y=39$ ---(2)

From (1)

$9x-10y=-12$

$\Rightarrow 9x=10y-12$

$\Rightarrow x=\frac{10y-12}{9}$

Substitute $x=\frac{10y-12}{9}$ in $2x+3y=39$

$\Rightarrow 2\left(\frac{10y-12}{9}\right)+3y=39$

$\Rightarrow 20y-24+27y=351$

$47y=375$

$\Rightarrow y=\frac{375}{47}$

Now, $x=\frac{10y-12}{9}$

$=\frac{10\left(\frac{375}{47}\right)-12}{9}$

$=\frac{3750-564}{47\times 9}$

$=\frac{3186}{47\times 9}$

$\Rightarrow x=\frac{354}{47}$

Therefore, $x=\frac{354}{47}$ and $y=\frac{375}{47}$