Question

2x+8y=8 and 2x-4y=-16 solved using elimination

Answer 1

To solve this system of equations using elimination, we can add the two equations together to eliminate the variable x.

Adding the two equations:

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

Now, we can divide the entire equation by 4 to simplify it:

x + y = -2

Now that we have the value of x + y, we can substitute back into one of the original equations to solve for x or y. Let's substitute into the first equation:

2x + 8y = 8
2(-2) + 8y = 8
-4 + 8y = 8
8y = 12
y = 1.5

Now that we have the value of y, we can substitute it back into the equation x + y = -2 to solve for x:

x + 1.5 = -2
x = -3.5

Therefore, the solution to the system of equations 2x + 8y = 8 and 2x - 4y = -16 is x = -3.5 and y = 1.5.