Question

Solve the system of equations.
2x+8y=8

2x−4y=−16
(1 point)

Answer 1

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

First, let's multiply the second equation by 2 to make the coefficients of x in both equations the same:

2(2x - 4y) = 2(-16)
4x - 8y = -32

Now we have:

2x + 8y = 8
4x - 8y = -32

Adding the two equations together:

(2x + 8y) + (4x - 8y) = 8 + (-32)
6x + 0y = -24
6x = -24

Dividing both sides of the equation by 6:

x = -24/6
x = -4

Now substitute the value of x into one of the original equations. Let's use the first equation:

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

Dividing both sides of the equation by 8:

y = 16/8
y = 2

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