Solve a System of Equations by Elimination -

$$\begin{gathered} 3x+8y=-3 \\ 2x+5y=-3 \end{gathered}$$

Equation - $$\begin{gathered} 3x+8y=-3 \\ 2x+5y=-3 \end{gathered}$$

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

Equation -

$$\begin{gathered} 3x+8y=-3 \\ 2x+5y=-3 \end{gathered}$$

We can eliminate y's by multiplying the first equation by 5 and second equation by 8 -

$$\begin{gathered} (3x+8y)\times 5=-3\times 5 \\ (2x+5y)\times 8=-3\times 8 \\ 15x+40y=-15 \\ 16x+40y=-24 \end{gathered}$$

The equation become -

$$\begin{gathered} 15x+40y=-15 \\ 16x+40y=-24 \end{gathered}$$

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

$\begin{array}{l}15x+40y=-15\\ \frac{16x+40y=-24}{-x=9}\end{array}$

Solve for x -

$x=-9$

Substitute $\mathit{x}\mathbf{=}\mathbf{-}\mathbf{9}$into the second equation localid="1647634245848" $\mathbf{2}\mathit{x}\mathbf{+}\mathbf{5}\mathit{y}\mathbf{=}\mathbf{-}\mathbf{3}$, Then Solve for y -

$$\begin{gathered} 2x+5y=-3 \\ 2\times -9+5y=-3 \\ -18+5y=-3 \\ 5y=-3+18 \\ 5y=15 \\ y=3 \end{gathered}$$

Written as $(x,y)$will be$(-9,3)$

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

Put $(-9,3)$in the equations -

$$\begin{gathered} 3x+8y=-3 \\ 3\times (-9)+8\times 3=-3 \\ -27+24=-3 \\ -3=-3 \\ 2x+5y=-3 \\ 2\times (-9)+5\times 3=-3 \\ -18+15=-3 \\ -3=-3 \end{gathered}$$

The Solution is - $\mathbf{(}\mathbf{-}\mathbf{9}\mathbf{,}\mathbf{3}\mathbf{)}$