Solve a system of equations using substitution
Use substitution when one equation is easy to isolate.
Do this: Read the concept below, then try the quiz or activity.
Lesson 82 of 192
42%
Concept
Solve one equation for a variable, substitute into the other equation, then back-substitute to find both values.
Try it
Solve y = 2x + 1 and x + y = 10.
⚖️ System Solver (2x2)
Use substitution steps and confirm with the solver.
Equation 1
2x + 1y = 9
Equation 2
1x - 1y = 1
Determinant: D = ae - bd = (2)(-1) - (1)(1) = -3
x = (ce - bf) / D = (9-1 - 1+1) / -3 = 3.333
y = (af - cd) / D = (2+1 - 9+1) / -3 = 2.333
Solution: (3.333, 2.333)
Common Misconception
Always verify your result in context instead of trusting a first pass.
Substitution method flow
These steps are out of order — can you fix them?
1.Back-substitute and verify
2.Solve for one variable
3.Substitute into other equation
4.Isolate a variable
Short Answer
When is substitution more efficient than elimination?
Mastery Check
Pass this check with at least 80% to unlock completion.
Pass the mastery check (80%+) to unlock completion.