Question

Solve a System of Equations by Elimination -

$$\begin{gathered} 7x+y=-4 \\ 13x+3y=4 \end{gathered}$$

Short answer

The simplification of Expression will be - $(-2,10)$.

Step-by-step solution

Step 1.  Given Information.

Equation -$$\begin{gathered} 7x+y=-4 \\ 13x+3y=4 \end{gathered}$$

Step 2.  To Find

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

Step 3.  Explanation

Equation -

$$\begin{gathered} 7x+y=-4 \\ 13x+3y=4 \end{gathered}$$

We can eliminate y's by multiplying the first equation by 3 -

$$\begin{gathered} (7x+y)\times 3=-4\times 3 \\ 13x+3y=4 \\ 21x+3y=-12 \\ 13x+3y=4 \end{gathered}$$

Step 4.  Calculation

The equation become -

$$\begin{gathered} 21x+3y=-12 \\ 13x+3y=4 \end{gathered}$$

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

$\begin{array}{l}21x+3y=-12\\ \frac{13x+3y=4}{8x=-16}\end{array}$

Solve for x -

$x=-2$

Substitute $\mathit{x}\mathbf{=}\mathbf{-}\mathbf{2}$into the second equation $\mathbf{13}\mathit{x}\mathbf{+}\mathbf{3}\mathit{y}\mathbf{=}\mathbf{4}$, Then Solve for y -

$$\begin{gathered} 13x+3y=4 \\ 13\times -2+3y=4 \\ -26+3y=4 \\ 3y=4+26 \\ 3y=30 \\ y=10 \end{gathered}$$

Written as $(x,y)$will be $(-2,10)$

Step 5.  Check the answer

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

Put $(-2,10)$in the equations -

$$\begin{gathered} 7x+y=-4 \\ 7\times (-2)+10=-4 \\ -14+10=-4 \\ -4=-4 \end{gathered}$$

$$\begin{gathered} 13x+3y=4 \\ 13\times (-2)+3\times 10=4 \\ -26+30=4 \\ 4=4 \end{gathered}$$

The Solution is - $\mathbf{(}\mathbf{-}\mathbf{2}\mathbf{,}\mathbf{10}\mathbf{)}$