Use the substitution method to determine whether the linear-quadratic system y=x2−9x+39 , y=9x−42 has 0, 1, or 2 solutions.(1 point)
To use the substitution method, we need to solve one equation for one variable and then substitute this expression into the other equation.
First, let's solve the second equation for y:
y = 9x - 42
Now, we can substitute this expression for y in the first equation:
x^2 - 9x + 39 = 9x - 42
Next, we simplify the equation:
x^2 - 18x + 81 = 0
This is a quadratic equation. Let's solve it using factoring:
(x - 9)(x - 9) = 0
We can see that the equation has one solution, x = 9.
Now, we can substitute this value of x back into one of the original equations to find the value of y:
y = 9(9) - 42 = 81 - 42 = 39
Therefore, the linear-quadratic system y = x^2 - 9x + 39 and y = 9x - 42 has one solution: (9, 39).