Question

Solve a System of Equations by Elimination -

$$\begin{gathered} 4x-3y=3 \\ 2x+5y=-31 \end{gathered}$$

Short answer

The simplification of Expression will be $(-3,-5)$.

Step-by-step solution

Step 1.  Given Information.

Equation - $$\begin{gathered} 4x-3y=3 \\ 2x+5y=-31 \end{gathered}$$

Step 2.  To Find

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

Step 3.  Explanation

Equation -

$$\begin{gathered} 4x-3y=3 \\ 2x+5y=-31 \end{gathered}$$

We can eliminate y's by multiplying the first equation by 5 and second equation by 3 -

$$\begin{gathered} (4x-3y)\times 5=3\times 5 \\ (2x+5y)\times 3=-31\times 3 \\ 20x-15y=15 \\ 6x+15y=-93 \end{gathered}$$

Step 4.  Calculation

The equation become -

$$\begin{gathered} 20x-15y=15 \\ 6x+15y=-93 \end{gathered}$$

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

localid="1647546161388" $\begin{array}{l}20x-15y=15\\ \frac{6x+15y=-93}{26x=-78}\end{array}$

Solve for x -

$x=-3$

Substitute $\mathit{x}\mathbf{=}\mathbf{3}$into the second equation $\mathbf{2}\mathit{x}\mathbf{+}\mathbf{5}\mathit{y}\mathbf{=}\mathbf{-}\mathbf{31}$, Then Solve for y -

$$\begin{gathered} 2x+5y=-31 \\ 2\times -3+5y=-31 \\ -6+5y=-31 \\ 5y=-31+6 \\ 5y=-25 \\ y=-5 \end{gathered}$$

Written as $(x,y)$will be $(-3,-5)$

Step 5.  Check the answer

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

Put $(-3,-5)$in the equations -

$$\begin{gathered} 4x-3y=3 \\ 4\times (-3)-3\times (-5)=3 \\ -12+15=3 \\ 3=3 \\ 2x+5y=-31 \\ 2\times (-3)+5\times (-5)=-31 \\ -6-25=-31 \\ -31=-31 \end{gathered}$$

The Solution is localid="1656119330551" $\mathbf{(}\mathbf{-}\mathbf{3}\mathbf{,}\mathbf{-}\mathbf{5}\mathbf{)}$