Question

In the following exercises, solve the systems of equations by elimination.

$$\begin{gathered} 5x-3y=-1 \\ 2x-y=2 \end{gathered}$$

Short answer

The solution for the system of linear equation is$\left(7,12\right)$.

Step-by-step solution

Step 1. Given Information

The system of linear equation:

$$\begin{gathered} 5x-3y=-1........\left(1\right) \\ 2x-y=2........\left(2\right) \end{gathered}$$

Step 2. Calculation

Here both equations are in standard form. To get opposite coefficients of y multiply second equation with $-3$.

$$\begin{gathered} -3\left(2x-y\right)=-3\left(2\right) \\ -6x+3y=-6.........\left(3\right) \end{gathered}$$

Solve for x:

From equations $\left(1\right)$and $\left(3\right)$:

role="math" localid="1644423137231" $$\begin{gathered} 5x-3y=-1 \\ \underline{-6x+3y=-6} \\ -x=-7 \\ x=7 \end{gathered}$$

Solve for y:

Substitute $x=7$

in the equation $5x-3y=-1$and solve for y.

$$\begin{gathered} 5x-3y=-1 \\ 5\left(7\right)-3y=-1 \\ 35-3y=-1 \\ -3y=-1-35 \\ -3y=-36 \\ y=\frac{-36}{-3} \\ y=12 \end{gathered}$$