Question

Solve the system of equation.

$\begin{array}{l}x+y=-3\\ 3x+4y=-12\end{array}$

Short answer

The solution is $x=0,y=-3$.

Step-by-step solution

Step 1- Consider the equation.

Consider the system of equation

$\begin{array}{l}x+y=-3\left(1\right)\\ 3x+4y=-12\left(2\right)\end{array}$

Step 2- Step description.

Multiply the equation (1) by 3 such that $3x+3y=-9$. (3)

Subtract the equation (3) from the equation (2) as follows:

$\begin{array}{c}3x+4y-(3x+3y)=-12-(-9)\\ 3x+4y-3x-3y=-12+9\\ y=-3\end{array}$

Step 3- Step description.

Substitute the value of y in equation (1).

$\begin{array}{c}x+y=-3\\ x+(-3)=-3\\ x-3=-3\\ x=-3+3\\ x=0\end{array}$

Therefore, the solution is $x=0,y=-3$.