Question

use elimination to solve the system of equations
$x - y = -8$
$7x + 5y = 16$
( , )
need help?

Explanation:

Step1: Multiply the first equation

To eliminate \( y \), multiply the first equation \( x - y = -8 \) by 5. We get \( 5(x - y)=5\times(-8) \), which simplifies to \( 5x - 5y = -40 \).

Step2: Add the two equations

Now add the new equation \( 5x - 5y = -40 \) to the second equation \( 7x + 5y = 16 \).
\((5x - 5y)+(7x + 5y)=-40 + 16\)
Simplifying the left - hand side: \(5x+7x-5y + 5y=12x\)
Simplifying the right - hand side: \(-40 + 16=-24\)
So we have the equation \(12x=-24\)

Step3: Solve for x

Divide both sides of \(12x=-24\) by 12: \(x=\frac{-24}{12}=-2\)

Step4: Substitute x into the first equation

Substitute \(x = - 2\) into the first equation \(x - y=-8\). We get \(-2-y=-8\)
Add 2 to both sides: \(-y=-8 + 2=-6\)
Multiply both sides by - 1: \(y = 6\)

Answer:

\((-2,6)\)