Question

5x−4y=34 −x+8y=22 elimination

Answer 1

Answer:

The solution to the system of equations is:

$x=10,\:y=4$

Step-by-step explanation:

Given the system of equations

$\begin{bmatrix}5x-4y=34\\ -x+8y=22\end{bmatrix}$

Multiply -x+8y=22 by 5:  -5x+40y=110

$\begin{bmatrix}5x-4y=34\\ -5x+40y=110\end{bmatrix}$

so adding the equations

$-5x+40y=110$

$+$

$\underline{5x-4y=34}$

$36y=144$

solve 36y = 144 for y:

$36y=144$

divide both sides by 36

$\frac{36y}{36}=\frac{144}{36}$

Simplify

$y=4$

For 5x-4y=34 plug in y=4

$5x-4\cdot \:4=34$

$5x-16=34$

Add 16 to both sides

$5x-16+16=34+16$

Simplify

$5x=50$

Divide both sides by 5

$\frac{5x}{5}=\frac{50}{5}$

Simplify

$x=10$

Therefore, the solution to the system of equations is:

$x=10,\:y=4$