Algebra 1 · Grades 8 to 9
Systems of equations
Find the pair that solves two equations at once.
The idea
A system of equations is two or more equations with the same variables. A solution is a pair of values that makes every equation true at the same time.
Substitution works well when one equation already gives you a variable by itself. Replace that variable in the other equation, then solve.
Worked examples
- How to Solve a System of Equations by Substitution Solve y = 2x + 1 and 3x + y = 11 by substitution. Five steps, the reason for each one, and the substitution mistakes to avoid.
- How to Solve a System of Equations by Elimination Solve 2x + 3y = 12 and x - y = 1 by elimination. Four steps, the add-the-equations method, and the multiply-one-term mistakes.
- Solve a System by Elimination with Multiplication Solve 4x + 3y = 18 and 2x - y = 4 by elimination. Five steps that build opposite coefficients before adding, with the setup mistakes.
Practice this topic
3 problems with answers.