When one equation is a line and the other a quadratic, use substitution. If y = x² + x − 18 and y = 2x + 2, set them equal: x² + x − 18 = 2x + 2.
Rearrange to a quadratic equal to 0: x² − x − 20 = 0, so (x − 5)(x + 4) = 0 and x = 5 or x = −4. Substitute each into the line: y = 12 or y = −6. The solutions (5, 12) and (−4, −6) are where the line crosses the curve.
Worked example
Solve y = x² + 6x + 17 and y = −2x + 2.
- x² + 6x + 17 = −2x + 2, so x² + 8x + 15 = 0.
- (x + 3)(x + 5) = 0: x = −3 gives y = 8; x = −5 gives y = 12.
Answer:(−3, 8) and (−5, 12)
Key words
- substitution
- replace y with an expression
- intersection
- where the graphs meet
- pair of solutions
- matching x and y values
Practise this
New questions every time.
Common Core-referenced: HSA-REI.C.7