Sure.
To find the ordered pair solutions for the system of equations f(x)=x²−2x−15 and f(x)=−x−9, we can use the following steps:
Solve the first equation for x.
Substitute the solution from step 1 into the second equation.
Solve the resulting equation for y.
The ordered pair (x,y) is the solution to the system of equations.
Solving the first equation for x, we get:
x = (-2 ± √(4 + 4(1)(-15))) / 2
x = (-2 ± √(-56)) / 2
x = (-2 ± 2√14) / 2
x = -1 ± √14
Substituting x=−1±√14 into the second equation, we get:
f(x) = -x-9
(-1 ± √14)² - 2(-1 ± √14) - 9 = -(-1 ± √14) - 9
1 ± 2√14 - 9 = -8 ± 2√14
Therefore, the ordered pair solutions for the system of equations f(x)=x²−2x−15 and f(x)=−x−9 are:
(-1 + √14, -8 + 2√14)
(-1 - √14, -8 - 2√14)