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

Solve the system of equations.

x
=
–
4
y
x
2
+
y
2
=
17

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
=
–
4
y
+
17
x
2
+
y
2
=
34

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:

–

Line

Circle

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

(

–

)

Apply the distributive property (FOIL)

–

136

289

Apply the distributive property (FOIL)

–

136

289

–

136

255

(

–

)

(

–

)

(

–

)

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 line

–

and the circle

intersect at two points:

(

–

)

and

(

)

Looking for more? Try these:

Lesson: Systems of equations

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Work it out

Not feeling ready yet? These can help:

O.8Solve a system of equations using substitution

Z.3Solve a quadratic equation by factoring

Lesson: Systems of equations

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