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
x-4=0
x-4+4=0+4
x=4

Substitute this into the first, linear, equation:
y=5(4)-9=20-9=11

Agc and bgd are vertical angles