Question

Use elimination to solve each system of equation.

$\begin{array}{c}\mathbf{3}\mathbf{x}\mathbf{+}\mathbf{7}\mathbf{y}\mathbf{=}\mathbf{2}\\ \mathbf{3}\mathbf{x}\mathbf{-}\mathbf{4}\mathbf{y}\mathbf{=}\mathbf{13}\end{array}$

Short answer

The solution of the given system of equations is $\mathbf{(}\mathbf{3}\mathbf{,}\mathbf{-}\mathbf{1}\mathbf{)}$.

Step-by-step solution

Step 1. Write the given system of equations.

The given system of equations is:

$\begin{array}{c}3x+7y=2....\left(1\right)\\ 3x-4y=13....\left(2\right)\end{array}$

Step 2. Solve the given system of equations.

Subtract the equation (2) from equation (1) to eliminate the variable $x$.

$\begin{array}{l}3x+7y=2\\ \text{3}x-4y=13\\ \underset{¯}{-+-}\\ \text{11}y=-11\\ y=\frac{-11}{11}\\ y=-1\end{array}$

The value $y$of is $-1$.

Substitute $-1$for$y$ in the equation (1) to find the value of $x$.

$\begin{array}{c}3x+7y=2\\ 3x+7(-1)=2\\ 3x-7=2\\ 3x=2+7\\ 3x=9\\ x=\frac{9}{3}\\ x=3\end{array}$

The value$x$of is 3.

Therefore, the solution of the given system of equations is $(3,-1)$.