MathAlgebraHigh frequency

SAT Math: Systems of Linear Equations from Word Problems

42+ practice questions in Praczo

What you need to know

The concept, explained

  • 1

    Many SAT word problems require you to set up two equations with two variables.

  • 2

    Usually, one equation is for the TOTAL quantity (e.g., x + y = Total Items), and the other is for VALUE (e.g., Cost_x*x + Cost_y*y = Total Cost).

  • 3

    Define your variables clearly BEFORE writing the equations (e.g., let a = adult tickets, c = child tickets).

  • 4

    Once set up, use either substitution or elimination to solve. Elimination is often faster for standard form equations.

  • 5

    Always double-check which variable the question is actually asking for; don't just solve for x and stop if it asked for y.

Common mistakes
  • Mixing up the coefficients (attaching the price of adult tickets to the variable for child tickets).
  • Solving the system correctly but selecting the value for the wrong variable.
Try a sample question

SAT-style practice

A store sells standard pens for (2 and premium pens for )5. If they sold 30 pens total for $90, how many standard pens did they sell?

42+ questions ready to practice

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