Q. 47 - Intermediate Algebra

Question

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

$$\begin{gathered} 6x-5y=-1 \\ 2x+y=13 \end{gathered}$$

Step-by-Step Solution

Answer

The solution for system of linear equation is that $\left(4,5\right)$.

Step 1. Given Information

The system of linear equation:

$$\begin{gathered} 6x-5y=-1 ........\left(1\right) \\ 2x+y=13 ........\left(2\right) \end{gathered}$$

Step 2. Calculation

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

$$\begin{gathered} 5\left(2x+y\right)=5\left(13\right) \\ 10x+5y=65 ........\left(3\right) \end{gathered}$$

Solve for x:

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

$$\begin{gathered} 6x-5y=-1 \\ \underline{10x+5y=65} \\ 16x=64 \\ x=\frac{64}{16} \\ x=4 \end{gathered}$$

Solve for y:

Substitute $x=4$ 

in the equation $6x-5y=-1$ and solve for y.

$$\begin{gathered} 6x-5y=-1 \\ 6\left(4\right)-5y=-1 \\ 24-5y=-1 \\ -5y=-1-24 \\ -5y=-25 \\ y=\frac{-25}{-5} \\ y=5 \end{gathered}$$