Systems of Equations — Two Equations, Two Unknowns
Heavily tested. You MUST be fast at these.
Method 1 — Substitution:
Solve one equation for a variable, plug into the other. Best when one equation is already solved: y = 3x + 2
Method 2 — Elimination:
Add or subtract equations to eliminate one variable.
2x + 3y = 12
2x - y = 4
Subtract: 4y = 8, y = 2, x = 3
Special cases:
No solution: Same slope, different y-intercepts (parallel lines)
Infinite solutions: Same line (equations are multiples of each other)
One solution: Different slopes (lines cross once)
SAT trick: Sometimes they ask for an expression like "x + y" — you can often get this directly from elimination without solving for individual variables.
Reference:
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