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Find the ordered pair solutions for the

system of equations.
f(x)=x²- 2x - 15
f(x) = -x-9
([?], 1) and (
Enter the smallest x first.

User Nick Bisby
by
7.6k points

1 Answer

3 votes

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)

User Ted Karmel
by
7.8k points

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