Question

Solve a System of Equations by Elimination -

$$\begin{gathered} -3x+5y=-13 \\ 2x+y=-26 \end{gathered}$$

Short answer

The simplification of Expression will be - $(-9,-8)$.

Step-by-step solution

Step 1.  Given Information.

Equation - $$\begin{gathered} -3x+5y=-13 \\ 2x+y=-26 \end{gathered}$$

Step 2.  To Find

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

Step 3.  Explanation

Equation -

$$\begin{gathered} -3x+5y=-13 \\ 2x+y=-26 \end{gathered}$$

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

$$\begin{gathered} -3x+5y=-13 \\ (2x+y)\times 5=-26\times 5 \\ -3x+5y=-13 \\ 10x+5y=-130 \end{gathered}$$

Step 4.  Calculation

The equation become -

$$\begin{gathered} -3x+5y=-13 \\ 10x+5y=-130 \end{gathered}$$

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

$\begin{array}{l}-3x+5y=-13\\ \frac{10x+5y=-130}{-13x=117}\end{array}$

Solve for x -

$x=-9$

Substitute localid="1647543694485" $\mathit{x}\mathbf{=}\mathbf{-}\mathbf{9}$into the second equation localid="1647543833859" $\mathbf{2}\mathit{x}\mathbf{+}\mathit{y}\mathbf{=}\mathbf{-}\mathbf{26}$, Then Solve for y -

$$\begin{gathered} 2x+y=-26 \\ 2\times -9+y=-26 \\ -18+y=-26 \\ y=-26+18 \\ y=-8 \end{gathered}$$

Written as $(x,y)$will be $(-9,-8)$

Step 5.  Check the answer

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

Put $(-9,-8)$in the equations -

$$\begin{gathered} -3x+5y=-13 \\ -3\times (-9)+5\times (-8)=-13 \\ 27-40=-13 \\ -13=-13 \end{gathered}$$

$$\begin{gathered} 2x+y=-26 \\ 2\times (-9)+(-8)=-26 \\ -18-8=-26 \\ -26=-26 \end{gathered}$$

The Solution is -$\mathbf{(}\mathbf{-}\mathbf{9}\mathbf{,}\mathbf{-}\mathbf{8}\mathbf{)}$