Question

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

$$\begin{gathered} 11x+9y=-5 \\ 7x+5y=-1 \end{gathered}$$

Short answer

The solution for the system of linear equation is $\left(2,-3\right)$.

Step-by-step solution

Step 1. Given Information

The system of linear equations:

$$\begin{gathered} 11x+9y=-5........\left(1\right) \\ 7x+5y=-1........\left(2\right) \end{gathered}$$

Step 2. Calculation

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

$$\begin{gathered} -5\left(11x+9y\right)=-5\left(-5\right) \\ -55x-45y=25.........\left(3\right) \end{gathered}$$

Also multiply second equation with 9.

$$\begin{gathered} 9\left(7x+5y\right)=9\left(-1\right) \\ 63x+45y=-9..........\left(4\right) \end{gathered}$$

Solve for x:

From equations $\left(3\right)$and $\left(4\right)$:

$$\begin{gathered} -55x-45y=25 \\ \underline{63x+45y=-9} \\ 8x=16 \\ x=\frac{16}{8} \\ x=2 \end{gathered}$$

Solve for y:

Substitute $x=2$

in the equation $11x+9y=-5$and solve for y.

$$\begin{gathered} 11x+9y=-5 \\ 11\left(2\right)+9y=-5 \\ 22+9y=-5 \\ 9y=-5-22 \\ 9y=-27 \\ y=\frac{-27}{9} \\ y=-3 \end{gathered}$$

The solution for the system of linear equation is $\left(2,-3\right)$.