This system has one solution. {y=5x-9y=x2-3x+7 What is the y-coordinate of the solution?

The y-coordinate of the solution is 11.

Both equations have y isolated. We will use substitution for this system:

5x-9=x²-3x+7

We want to gather all of the variables on one side, so we will subtract 5x from each side:

5x-9-5x=x²-3x+7-5x

-9=x²-8x+7

We want the equation to be equal to 0 to solve it, so we will add 9 to both sides:

-9+9=x²-8x+7+9

0=x²-8x+16

This is easy to factor; factors of 16 that sum to - 8 are - 4 and - 4:

0 = (x-4) (x-4)

Since these are the same factor, we solve it to get our answer:

x-4=0

x-4+4=0+4

x=4

Substitute this into the first, linear, equation:

y=5 (4) - 9=20-9=11