Back

Systems of Linear Equations

SAT MathAlgebraMedium

Use substitution, elimination, or graphing according to the system’s structure.

What you need to know

  • A solution is an ordered pair satisfying both equations.
  • Substitution is efficient when a variable is isolated.
  • Elimination is efficient when coefficients match or are easy multiples.
  • Parallel distinct lines give no solution; the same line gives infinitely many.

The AYLOTI method

  1. Choose the shorter method.
  2. Solve for one variable.
  3. Substitute back for the other.
  4. Check the ordered pair in both original equations.

AYLOTI • Sir Hunain Zia • SAT Score 1594/1600 • 154 Total A Grades (Personal), 11 World Records, 7 Distinctions

Worked example

Solve x + y = 11 and 2x − y = 4.

  1. Add equations to eliminate y: 3x = 15.
  2. x = 5.
  3. Substitute: 5 + y = 11, so y = 6.

Answer: (5, 6).

Common SAT traps

  • Returning only x when an ordered pair is required.
  • Adding equations without aligning like terms.
  • Interpreting a graphing-window miss as no intersection.
Quick check

Solve y = 2x + 1 and y = 2x − 4.

No solution; the lines are parallel.

Before you move on

  • Explain the core rule without looking back.
  • Redo the worked example using your own steps.
  • Write the trap you are most likely to fall for.
author avatar