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.
- Line the equations up and look at the coefficients.
- If adding or subtracting the equations gives exactly what is asked (such as x + y), do that and stop.
- Otherwise eliminate one variable, solve for the other, and substitute back.
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.)
- 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.
Every practice question comes with a full explanation, including why each wrong choice is wrong. Free, with no account.