Question

Solve a System of Equations by Elimination -

$$\begin{gathered} 5x-7y=29 \\ x+3y=-3 \end{gathered}$$

Short answer

The simplification of Expression will be - $(3,-2)$.

Step-by-step solution

Step 1.  Given Information.

Equation - $$\begin{gathered} 5x-7y=29 \\ x+3y=-3 \end{gathered}$$

Step 2.  To Find

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

Step 3.  Explanation

Equation -

$$\begin{gathered} 5x-7y=29 \\ x+3y=-3 \end{gathered}$$

We can eliminate y's by multiplying the first equation by 3 and second equation by 7 -

$$\begin{gathered} (5x-7y)\times 3=29\times 3 \\ (x+3y)\times 7=-3\times 7 \\ 15x-21y=87 \\ 7x+21y=-21 \end{gathered}$$

Step 4.  Calculation

The equation become -

$$\begin{gathered} 15x-21y=87 \\ 7x+21y=-21 \end{gathered}$$

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

$\begin{array}{l}15x-21y=87\\ \frac{7x+21y=-21}{22x=66}\end{array}$

Solve for x -

$x=3$

Substitute localid="1647459385023" $\mathit{x}\mathbf{=}\mathbf{3}$into the second equation $\mathit{x}\mathbf{+}\mathbf{3}\mathit{y}\mathbf{=}\mathbf{-}\mathbf{3}$, Then Solve for y -

localid="1647460424425" $$\begin{gathered} x+3y=-3 \\ 3+3y=-3 \\ 3y=-3-3 \\ 3y=-6 \\ y=-2 \end{gathered}$$

Written as $(x,y)$will be role="math" localid="1649173304812" $(3,-2)$.

Step 5.  Check the answer

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

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

$$\begin{gathered} 5x-7y=29 \\ 5\times 3-7\times (-2)=29 \\ 15+14=29 \\ 29=29 \end{gathered}$$

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

The Solution is - $(3,-2)$