Systems of Linear Equations
Three Methods
1. Substitution — solve one equation for a variable, plug into the other
2. Elimination — add/subtract equations to cancel a variable
3. Graphing — intersection point is the solution
Number of Solutions
One solution — lines intersect (different slopes)
No solution — lines are parallel (same slope, different y-intercept)
Infinite solutions — same line (same slope AND y-intercept)
a₁/a₂ ≠ b₁/b₂ → one solution | a₁/a₂ = b₁/b₂ ≠ c₁/c₂ → no solution | a₁/a₂ = b₁/b₂ = c₁/c₂ → infinite
SAT Strategy
Look for which method is fastest — don't default to one
Elimination is often fastest on the SAT
Watch for "what is x + y?" questions — you may not need individual values