Question

Solve a System of Equations by Elimination -

$$\begin{gathered} 5x-3y=-1 \\ 2x-y=2 \end{gathered}$$

Short answer

The simplification of Expression will be - $(7,12)$.

Step-by-step solution

Step 1.  Given Information.

Equation - $$\begin{gathered} 5x-3y=-1 \\ 2x-y=2 \end{gathered}$$

Step 2.  To Find

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

Step 3.  Explanation

Equation -

$$\begin{gathered} 5x-3y=-1 \\ 2x-y=2 \end{gathered}$$

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

$$\begin{gathered} 5x-3y=-1 \\ (2x-y)\times 3=2\times 3 \\ 5x-3y=-1 \\ 6x-3y=6 \end{gathered}$$

Step 4.  Calculation

The equation become -

$$\begin{gathered} 5x-3y=-1 \\ 6x-3y=6 \end{gathered}$$

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

$\begin{array}{l}5x-3y=-1\\ \frac{6x-3y=6}{-x=-7}\end{array}$

Solve for x -

$x=7$

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

$$\begin{gathered} 2x-y=2 \\ 2\times 7-y=2 \\ 14-y=2 \\ -y=2-14 \\ y=12 \end{gathered}$$

Written as $(x,y)$will be $(7,12)$

Step 5.  Check the answer

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

Put $(7,12)$in the equations -

$$\begin{gathered} 5x-3y=-1 \\ 5\times 7-3\times 12=-1 \\ 35-36=-1 \\ -1=-1 \end{gathered}$$

$$\begin{gathered} 2x-y=2 \\ 2\times 7-12=2 \\ 14-12=2 \\ 2=2 \end{gathered}$$

The Solution is - $\mathbf{(}\mathbf{7}\mathbf{,}\mathbf{12}\mathbf{)}$