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

Solve the system of equations.

x
2
+
y
2
=
5
y
=
–
3
x
–
5

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.

x
2
+
y
2
=
20
y
=
–
2
x

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:

Circle

–

Line

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

Notice that the equation of the circle has an

term and a

term. You can't avoid squaring, so it doesn't matter if you isolate

in the linear equation. Luckily,

is already isolated:

–

Substitute

–

into the equation of the circle and solve for

(

–

)

±2

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 circle

and the line

–

intersect at two points:

(

–

)

and

(

–

)

Looking for more? Try these:

Lesson: Systems of 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

Lesson: Systems of equations

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