Question

Solve the system of equation.

$\begin{array}{l}3x+5y=2\\ 2x-y=-3\end{array}$

Short answer

The solution is $x=-1,y=1$.

Step-by-step solution

Step 1- Consider the equation.

Consider the system of equation

$\begin{array}{l}3x+5y=2\left(1\right)\\ 2x-y=-3\left(2\right)\end{array}$

Step 2- Step description.

Multiply the equation (2) by 5 such that $10x-5y=-15$. (3)

Add the equation (3) and the equation (1) as follows:

$\begin{array}{l}10x-5y+3x+5y=-15+2\\ 13x=-13\\ x=-1\end{array}$

Step 3- Step description.

Substitute the value of x in equation (1).

$\begin{array}{l}3x+5y=2\\ 3(-1)+5y=2\\ -3+5y=2\\ 5y=2+3\\ y=1\end{array}$

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