Solve a System of Equations by Elimination -

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

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

Solve a System of Equations by Elimination and find the value of x and y.

Equation -

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

We can eliminate y's by multiplying the first equation by 5 and second equation by 9 -

$$\begin{gathered} (11x+9y)\times 5=-5\times 5 \\ (7x+5y)\times 9=-1\times 9 \\ 55x+45y=-25 \\ 63x+45y=-9 \end{gathered}$$

The equation become -

$$\begin{gathered} 55x+45y=-25 \\ 63x+45y=-9 \end{gathered}$$

We subtract the x's and y's and constants -

$\begin{array}{l}55x+45y=-25\\ \frac{63x+45y=-9}{-8x=-16}\end{array}$

Solve for x -

$x=2$

Substitute $\mathit{x}\mathbf{=}\mathbf{2}$into the second equation $\mathbf{7}\mathit{x}\mathbf{+}\mathbf{5}\mathit{y}\mathbf{=}\mathbf{-}\mathbf{1}$, Then Solve for y -

$$\begin{gathered} 7x+5y=-1 \\ 7\times 2+5y=-1 \\ 14+5y=-1 \\ 5y=-1-14 \\ 5y=-15 \\ y=-3 \end{gathered}$$

Written as $(x,y)$will be $(2,-3)$

Check that the ordered pair is a solution to both original equations -

Put $(2,-3)$in the equations -

$$\begin{gathered} 11x+9y=-5 \\ 11\times 2+9\times (-3)=-5 \\ 22-27=-5 \\ -5=-5 \\ 7x+5y=-1 \\ 7\times 2+5\times (-3)=-1 \\ 14-15=-1 \\ -1=-1 \end{gathered}$$

The Solution is - $\mathbf{(}\mathbf{2}\mathbf{,}\mathbf{-}\mathbf{3}\mathbf{)}$