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

Objective: Students will solve systems using substitution and verify solutions.

Estimated Time: 12 minutes

Standards:
HSA-REI.C.6HSA-REI.D.10

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)

Concept Check

Best first step for y = 3x - 2 and x + y = 6 is:

Concept Check

After finding x in substitution, you must:

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.

Question 1

Best first step for y = 3x - 2 and x + y = 6 is:

Question 2

After finding x in substitution, you must:

Pass the mastery check (80%+) to unlock completion.