Solving a system by substitution
Solve one equation for a variable and substitute it into the other.
The common mistake
Substituting back into the same equation you rearranged, which gives 0 = 0 and no answer.
Instead: Rearrange one equation, substitute into the other one, solve, then plug back in for the second variable.
Worked example with Guide me
Solve y = 2x and x + y = 9.
- Sugar · Replace y in the second equation.Student · x + 2x = 9.
- Sugar · Solve for x.Student · 3x = 9, so x = 3.
- Sugar · Now find y.Student · y = 2(3) = 6.
Answer: (3, 6)
Try 3 practice questions
1. Solve y = x + 1 and 2x + y = 10.
Show answer
(3, 4)
2. Solve x = 3y and x + y = 8.
Show answer
(6, 2)
3. Solve y = 4 − x and y = x + 2.
Show answer
(1, 3)
Quick answers
- What is the most common mistake with solving a system by substitution?
- Substituting back into the same equation you rearranged, which gives 0 = 0 and no answer.
- How do I get solving a system by substitution right?
- Rearrange one equation, substitute into the other one, solve, then plug back in for the second variable.
- Can you show a worked example?
- Solve y = 2x and x + y = 9. (3, 6)
Related concepts
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