Question

Solve a System of Equations by Elimination -

$$\begin{gathered} 4x+7y=14 \\ -2x+3y=32 \end{gathered}$$

Short answer

The simplification of Expression will be - $(-7,6)$.

Step-by-step solution

Step 1.  Given Information.

Equation -$$\begin{gathered} 4x+7y=14 \\ -2x+3y=32 \end{gathered}$$

Step 2.  To Find

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

Step 3.  Explanation

Equation -

$$\begin{gathered} 4x+7y=14 \\ -2x+3y=32 \end{gathered}$$

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

$$\begin{gathered} (4x+7y)\times 3=14\times 3 \\ (-2x+3y)\times 7=32\times 7 \\ 12x+21y=42 \\ -14x+21y=224 \end{gathered}$$

Step 4.  Calculation

The equation become -

$$\begin{gathered} 12x+21y=42 \\ -14x+21y=224 \end{gathered}$$

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

$\begin{array}{l}12x+21y=42\\ \frac{-14x+21y=224}{26x=-182}\end{array}$

Solve for x -

localid="1647546792662" $x=-7$

Substitute $\mathit{x}\mathbf{=}\mathbf{-}\mathbf{7}$into the second equation localid="1647546840941" $\mathbf{-}\mathbf{2}\mathit{x}\mathbf{+}\mathbf{3}\mathit{y}\mathbf{=}\mathbf{32}$, Then Solve for y -

$$\begin{gathered} -2x+3y=32 \\ -2\times -7+3y=32 \\ 14+3y=32 \\ 3y=32-14 \\ 3y=18 \\ y=6 \end{gathered}$$

Written as $(x,y)$will be$(-7,6)$

Step 5.  Check the answer

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

Put $(-7,6)$in the equations -

$$\begin{gathered} 4x+7y=14 \\ 4\times (-7)+7\times 6=14 \\ -28+42=14 \\ 14=14 \\ -2x+3y=32 \\ -2\times (-7)+3\times 6=32 \\ 14+18=32 \\ 32=32 \end{gathered}$$

The Solution is -$\mathbf{(}\mathbf{-}\mathbf{7}\mathbf{,}\mathbf{6}\mathbf{)}$