Question

Solve: $3x+2y=15$ and $10x-4y=2$

Answer 1

Given equations can be written as,

$3x+2y-15=0\dots \left(i\right)$

$10x-4y-2=0\dots \left(ii\right)$

Multiply $\left(i\right)$ by $2$ and add it in equation $\left(ii\right),$

$\begin{array}{cc}2\left(3x+2y-15\right)+\left(10x-4y-2\right)& =0\\ 6x+4y-30+10x-4y-2& =0\\ 16x-32& =0\\ 16x& =32\\ x& =2\end{array}$

Substitute $x=2$ in equation $\left(i\right),$

$\begin{array}{cc}3\times 2+2y& =15\\ 6+2y& =15\\ 2y& =15-6\\ 2y& =9\\ y& =\frac{9}{2}\end{array}$

Therefore $x=2$ and $y=\frac{9}{2}$ is the solution for the given pair of equation.