Question

Find the y-coordinate of the solution to the following system of equations.

-4x + 12y = 0

12x + 4y = 160

Answer 1

To find the y-coordinate of the solution, we need to solve the system of equations. We can do this by either substitution or elimination.

Let's solve using elimination. We can multiply the first equation by 3 and the second equation by -1 to eliminate the x variable:

-4x + 12y = 0 (multiply by 3)
12x + 4y = 160 (multiply by -1)

This gives us:
-12x + 36y = 0
-12x - 4y = -160

Now we can subtract the second equation from the first equation:

( -12x + 36y ) - ( -12x - 4y ) = 0 - (-160)
-12x + 36y + 12x + 4y = 0 + 160

Simplifying this, we get:
40y = 160

Dividing both sides by 40, we find:
y = 4

Therefore, the y-coordinate of the solution is 4.