Solving Systems of Equations: 3 Methods Compared
Substitution, elimination, or graphing? Learn when to use each method and save time on test day.
Why This Matters
Systems of equations appear in 3–5 questions per SAT Math section. Choosing the right method can save you 2+ minutes — which adds up fast.
Method 1: Substitution
Best when: one variable is already isolated (e.g., \(y = 3x + 2\)).
Plug the expression directly into the other equation. Solve for one variable, then back-substitute.
Method 2: Elimination
Best when: coefficients are easy to match (e.g., \(2x + 3y = 7\) and \(4x - 3y = 5\)).
Add or subtract equations to cancel one variable. This is usually the fastest method on the SAT.
Method 3: Graphing (Desmos)
Best when: the question asks for the intersection point or you're stuck.
On the digital SAT, Desmos is built in. Type both equations and tap the intersection. It's free — use it.
Decision Flowchart
- Is a variable already isolated? → Substitution
- Can I easily match coefficients? → Elimination
- Am I stuck or the numbers are ugly? → Desmos
Common Mistake
Students waste time trying to use substitution when elimination would take 10 seconds. Read both equations first before picking a method.
Practice
Try solving \(3x + 2y = 16\) and \(x - 2y = 0\) with all three methods. Notice which one feels fastest.