This system has one solution what is the y-coordinate of the solution y=5x-20 y=x^2-9x+29

y = 15

Step-by-step explanation:

Even tho' we're supposed to find y here, it's easier to eliminate y first, find x and then go back and calculate y.

Both given formulas have already been solved for y:

y=5x-20 and y=x^2-9x+29

We can equate them: 5x-20 = x^2-9x+29.

Next, move the terms 5x - 20 to the right side:

0 = x^2-9x+29 - 5x + 20, or

0 = x^2 - 14x + 49

This last result is the square of a binomial: the square of x - 7.

Thus, there are two identical, real solutions: {7, 7}.

Now go back to y = 5x - 20, substitute 7 for x and calculate the y-coordinate:

y = 5 (7) - 20 = 15

The y coordinate of the solution is 15.