Answer:
y = 2
x = -6
Step-by-step explanation:
Looking at the two equations, we notice right away that we can re-arrange the first equation to solve for x.
x + 4y = 2 becomes x = 2 - 4y
Now, we see that the second equation has an x in it. We replace the x in the second equation with the value of x we just found (using the first equation).
-x + y = 8 becomes -(2 - 4y) + y = 8
Simplify the left side!
1. Distribute the negative
-2 +4y + y = 8
2. Simplify like terms
-2 + 5y = 8
3. Move the -2 to the right side (changing its sign as we do so)
5y = 8 + 2
5y = 10
4. Divide both sides by 5
y = 2
NOW TO FIND X
Since we have the value for y, we can plug it in an equation to find x. We will use the second equation.
-x + y = 8 becomes -x +2 = 8
1. Move the 2 to the right side:
-x = 8 - 2
-x = 6
2. Divide both sides by -1:
x = -6
Now we come to a very important step: we must check our answers. First, we will plug in our numbers for x and y into the first equation.
x + 4y = 2
(-6) + 4(2) = 2
-6 + 8 = 2
2 = 2
The variables hold true for that equation. Now we check them with the second equation!
-x + y = 8
-(-6) + 2 = 8
6 + 2 = 8
8 = 8
Both our answers are right!
Hope this helped!!!