Step-by-step explanation:
We will solve this system of equations using two methods: elimination and substitution.
Method 1: Elimination
2x - y = -8. #1
-5x + y = 26. #2
Note that by adding these two equations, the y-variable is eliminated (thus the name) and you're only left with an equation with one variable. So upon adding, we get
-3x = 18 or x = -6
Using this value for x, put this back in either one of the equations. Let's use the 2nd one.
-5(-6) + y = 26
--> 30 + y = 26
Moving 30 to the right side, we get y = -4.
Method 2: Substitution
This is done by isolating one variable to the left side in one equation and then using it on the other equation. Let's take equation #2 and put the y-variable on the left side and you should get
y = 5x + 26
Now use this equation and plug it into the y in equation #1:
2x - (5x + 26) = -8
--> 2x - 5x - 26 = -8
--> -3x = 26 - 8 = 18 or x = -6.
Use this value for x into either one of the equations. Let's use equation #1 this time.
2(-6) - y = -8
--> -12 + 8 = y or y = -4.
Notice that using either method will give you the same result, as one might expect.
