Question

Can someone please professionally explain the math equations below. (Not just answer the question)

Answer 1

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.