Question

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

$$\begin{gathered} 2x-5y=7 \\ 3x-y=17 \end{gathered}$$

Short answer

The solution for the system of linear equation is$\left(6,1\right)$.

Step-by-step solution

Step 1. Given Information

The system of linear equation:

$$\begin{gathered} 2x-5y=7..........\left(1\right) \\ 3x-y=17..........\left(2\right) \end{gathered}$$

Step 2. Calculation

Here both equations are in standard form. To get opposite coefficients of y multiply second equation with $-5$.

$$\begin{gathered} -5\left(3x-y\right)=-5\left(17\right) \\ -15x+5y=-85........\left(3\right) \end{gathered}$$

Solve for x:

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

$$\begin{gathered} 2x-5y=7 \\ \underline{-15x+5y=-85} \\ -13x=-78 \\ x=\frac{-78}{-13} \\ x=6 \end{gathered}$$

Solve for y:

Substitute $x=6$

in the equation $2x-5y=7$and solve for y.

$$\begin{gathered} 2x-5y=7 \\ 2\left(6\right)-5y=7 \\ 12-5y=7 \\ -5y=7-12 \\ -5y=-5 \\ y=1 \end{gathered}$$