Students learn to solve a system of two linear equations — finding the single point (x, y) that satisfies both — and discover that graphically, the solution is exactly where the two lines intersect.
Students will be able to…
Two equations, two unknowns — is there one pair of values that makes BOTH true at once? What does that look like on a graph?
Project this and adjust both lines. The green dot marks the solution — the point that lies on BOTH lines. Watch what happens when they’re parallel!
Tap any phase to open the teacher moves and student actions.
Can one (x, y) make two different equations true at once?
Teacher models.
Class uses Where Lines Cross.
Students solve systems.
One system.
Aligned to the Common Core State Standards for Mathematics (High School: Algebra I).
Solve systems of linear equations exactly and approximately.
Explain that the solution is the intersection of the graphs.
Prove that replacing one equation by a sum produces a system with the same solutions.
Represent constraints by systems of equations.
Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.
Have students solve a system algebraically using substitution or elimination, then check against the graph. A printable systems sheet is in the Math library.
Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.
A quick self-check with instant feedback, drawn from this lesson’s key terms.
A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.