A line crosses a parabola twice, and finding where is substitution rather than elimination. These free printable worksheets set the two equations equal and let the quadratic that falls out do the rest.
If they get stuck
The answer key prints on a separate page.
Elimination is the reflex from linear systems and it does not apply here. Both equations say what y is, so wherever the graphs meet the two right-hand sides are equal — that is the substitution, and it is one line. What follows is an ordinary quadratic, collected to zero and factored.
Every quadratic on these sheets factors over the integers. That is the right call for this topic: the standard is about the substitution step, and a last line that needs the quadratic formula tests the previous lesson instead. The messier ones live on the solving-quadratics pages.
Find the x-values where y = x² − 7x + 7 meets y = −2x + 3
