Q. 4.18 - Intermediate Algebra

Question

Solve the system by elimination: $\left\{\begin{array}{l}4x+y=-5\\ -2x-2y=-2\end{array}\right.$

Step-by-Step Solution

Answer

The solution of the system of equations is $(-2,3)$.

Step 1. Given Information.

We have been given the system of equations $\left\{\begin{array}{l}4x+y=-5\\ -2x-2y=-2\end{array}\right.$.

Step 2. Eliminate y by multiplying a number in the first equation.

Multiply both sides of $4x+y=-5$ by 2.

$\left\{\begin{array}{l}2(4x+y)=2(-5)\\ -2x-2y=-2\end{array}\right.$

And,

$\left\{\begin{array}{l}8x+2y=-10\\ -2x-2y=-2\end{array}\right.$

Step 3. Add the equations resulting from Step 2 to eliminate one variable and solve it.

Add the $x\text{'}s,y\text{'}s$ and constants.

$\left\{\begin{array}{l}8x+2y=-10\\ -2x-2y=-2\end{array}\right.$

$6x=-12$

$x=-2$

Step 4. Substitute the solution from Step 3 into one of the original equation and solve for the other variable.

Substitute $x=-2$ into the first equation.

$4x+y=-5$

$4(-2)+y=-5$

$-8+y=-5$

$y=3$

Step 5. Write the solution as an ordered pair.

Write it as $(x,y).$

$(-2,3)$

Step 6. Check that the ordered pair is a solution to both original equations.

Substitute $x,y=-2,3$ into both original equations.

$4x+y=-5$

$4(-2)+3=-5$

$-8+3=-5$

$-5=-5$

And, 

$-2x-2y=-2$

$-2(-2)-2\left(3\right)=-2$

$4-6=-2$

$-2=-2$

Both equations are True. 

The point $(-2,3)$ is the solution to the system.