solve the system of equations: 2x+8y=8 , 2x-4y=-16

Answer 1

To solve this system of equations, we can use the method of elimination.

Given equations:
1. 2x + 8y = 8
2. 2x - 4y = -16

To use the elimination method, we will add both equations together. We get:

(2x + 8y) + (2x - 4y) = 8 + (-16)
4x + 4y = -8
x + y = -2

Now we have a new equation:
3. x + y = -2

Next, we can rearrange equation 3 to express x in terms of y, which gives us:
x = -2 - y

Now we can substitute this value of x into one of the original equations. Let's use equation 1:

2x + 8y = 8
2(-2 - y) + 8y = 8
-4 - 2y + 8y = 8
6y - 4 = 8
6y = 12
y = 2

Now that we know y, we can substitute back into equation 3 to solve for x:
x = -2 - 2
x = -4

Therefore, the solution to the system of equations is x = -4 and y = 2.