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This system has one solution. {y=5x−9y=x2−3x+7 What is the y-coordinate of the solution?
5 months ago
Q:
This system has one solution. {y=5x−9y=x2−3x+7 What is the y-coordinate of the solution?
Accepted Solution
A:
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