Lessons · Quantitative Reasoning

CLT Quantitative Reasoning · Lesson

Systems of equations

Two equations, two unknowns. Solve by elimination (add or subtract the equations) or substitution. Often the question asks for a combination you can get without solving fully.

How to do it
  1. Line the equations up and look at the coefficients.
  2. If adding or subtracting the equations gives exactly what is asked (such as x + y), do that and stop.
  3. Otherwise eliminate one variable, solve for the other, and substitute back.
Example

Q. 3x + 2y = 16 and x + 2y = 8. What is x + y?

Answer 6

Add the equations: 4x + 4y = 24, so x + y = 6. (Solving fully gives x = 4, y = 2; same answer, more work.)

Traps
  • Stopping after finding x when the question asks for y or x + y.
  • Subtracting a whole equation but forgetting to subtract the right-hand side.
Practice it

Every practice question comes with a full explanation, including why each wrong choice is wrong. Free, with no account.