Systems of Two Linear Equations
A system's solution is wherever two lines meet. Line 1 is fixed at y = x + 1 — adjust line 2's slope and intercept to see the three possible outcomes: one solution, no solution, or infinitely many.
Two linear equations, graphed together, can relate in exactly three ways. Different slopes means the lines cross exactly once — one solution. Same slope, different intercept means the lines are parallel and never meet — no solution. Same slope and same intercept means they’re the same line — infinitely many solutions.
You won’t always get to graph it on the SAT. Substitution and elimination — solving one equation for a variable and plugging it into the other, or adding/subtracting the equations to cancel a variable — get you to the same intersection point algebraically.
A common trick question: two equations that look different but simplify to the same line (infinitely many solutions), or the same slope in disguise (no solution). Rewriting both equations in the same form before comparing slopes avoids that trap.