# 2.08 Quadratic systems of equations

## Interactive practice questions

Solve the following equations simultaneously.

 Equation $1$1 $y=x^2+3x$y=x2+3x Equation $2$2 $y=-x+21$y=−x+21
a

First solve for $x$x.

b

Find the value of $y$y at the point of intersection where $x=3$x=3.

c

Find the value of $y$y at the point of intersection where $x=-7$x=7.

Easy
Approx 4 minutes

When solving $y=x^2-3x+1$y=x23x+1 and $y=x+6$y=x+6 simultaneously, one point of intersection is at $x=-1$x=1. What is the $y$y-coordinate at this point?

Solve the following equations simultaneously :

 Equation 1 $y=-2x-1$y=−2x−1 Equation 2 $y=x^2-8x+8$y=x2−8x+8

Solve the following equations simultaneously.

 Equation 1 $y=x^2$y=x2 Equation 2 $y=-7x$y=−7x

### Outcomes

#### A.REI.D.11^

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) =g(x); find the solutions approximately. ^Combine polynomial, rational, radical, absolute value, and exponential functions