Mathematics: 5x−4y=34 −x+8y=22 elimination

i know this is late but give me lolStep-by-step explanation:...

5x−4y=34 −x+8y=22 elimination - id543482210830243, jenhowie2944

NetherisIsTheQueen

18.03.2022

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:

$x=10,\:y=4$

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