Substitute the linear equation into the quadratic one, solve the quadratic, then find the matching values.
What you will learn
- Solve a line with a parabola
- Solve a line with a circle or with xy = k
- Use the discriminant to count meeting points
Substitute, then solve a quadratic
- y = x² − 3 and y = 2x
- x² − 3 = 2x
- x² − 2x − 3 = 0
- (x − 3)(x + 1) = 0, so x = 3 or x = −1
- pairs: (3, 6) and (−1, −2)
There are usually two solutions: two points where the line crosses the curve. Find y for each x using the linear equation.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Substitute, then solve a quadratic
- Circles, and counting the crossings
- Try it: See the line meet the curve
7 practice questions, marked as you go; about 25 minutes in all.
In this unit: Simultaneous equations
Solve two equations at once by elimination, substitution and graphs, form them from problems, and (Higher) solve a linear and a quadratic equation together.
- Solving by elimination
- Solving by substitution
- Solving with graphs
- Forming simultaneous equations
- A linear and a quadratic equation