Question

Solve the system of equation.

$\begin{array}{l}3x-2y=-2\\ 4x+7y=65\end{array}$

Short answer

The solution is $x=4,y=7$.

Step-by-step solution

Step 1- Consider the equation.

Consider the system of equation

$\begin{array}{l}3x-2y=-2\left(1\right)\\ 4x+7y=65\left(2\right)\end{array}$

Step 2- Step description.

Multiply the equation (2) by 3 and the equation (1) by 4.

$\begin{array}{l}12x-8y=-8\left(3\right)\\ 12x+21y=195\left(4\right)\end{array}$

Subtract the equation (3) from the equation (4) as follows:

$\begin{array}{l}12x+21y-(12x-8y)=195+8\\ 12x+21y-12x+8y=203\\ 29y=203\\ y=7\end{array}$

Step 3- Step description.

Substitute the value of y in equation (1).

$\begin{array}{l}3x-2y=-2\\ 3x-2\left(7\right)=-2\\ 3x-14=-2\\ 3x=12\\ x=4\end{array}$

Therefore, the solution is $x=4,y=7$.