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 2x + 3 = 11 Solve the two-step equation 2x + 3 = 11 in four steps. See the answer, why each step is allowed, and the mistakes to avoid.
- How to Solve an Equation with Variables on Both Sides Solve 5x - 4 = 3x + 8 in five steps. Collect the variables on one side, then check the answer in the original equation.
Practice this topic
3 problems with answers.