# How do you find the exact solutions to the system #y+x^2=3# and #x^2+4y^2=36#?

##### 2 Answers

The solutions are

#### Explanation:

Solve for y:

Substitute

Write as the product of two binomials.

Find the corresponding

Hence, the solutions are,

Note that there are three solutions, which means there are three points of intersection between the parabola

Three points of intersection

#### Explanation:

Given:

Subtract the first equation from the second:

Subtract 33 from both sides:

Compute the discriminant:

For

For