IXL - Solve a system of linear and quadratic equations: parabolas (Algebra 2 practice)

Solve the system of equations.

y
=
–
12
x
–
17
y
=
x
2
+
2
x
+
32

Write the coordinates in exact form. Simplify all fractions and radicals.

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Learn with an example

question

Solve the system of equations.

y
=
3
x
2
–
2
x
–
28
y
=
–
2
x
–
1

Write the coordinates in exact form. Simplify all fractions and radicals.

key idea

If a system of equations includes a linear equation and a quadratic equation (parabola, circle, ellipse, or hyperbola), then solve using

substitution.

solution

Look at the system of equations:

–

Parabola

–

Line

Since there is a linear equation, it's best to use substitution.

Notice that the parabolic equation has an

term, but no

term. To avoid squaring, it's best to isolate

in the linear equation. Luckily, it's already isolated:

–

Substitute

–

into the parabolic equation and solve for

–

±3

Finally, plug

and

–

into one of the original equations to find the solutions. It's easier to use the linear equation.

Plug in

–

(

)

–

The solution is

(

–

)

Plug in

–

(

–

)

–

The solution is

(

–

)

So, the parabola

–

and the line

–

intersect at two points:

(

–

)

and

(

–

)

Looking for more? Try these:

Lesson: Systems of equations

Lesson: Factoring quadratic equations

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Teacher tools

Work it out

Not feeling ready yet? These can help:

E.10Solve a system of equations using any method

O.3Solve a quadratic equation by factoring

P.1Solve a system of linear and quadratic equations by graphing: parabolas

Lesson: Systems of equations

Lesson: Factoring quadratic equations

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