PEAZIT Aha card
Go straight to resources ↓Simultaneous equations: one pair meets two conditions
A solution must satisfy both equations at once. Adding suitable equations can remove one unknown.
| Condition | Substitution |
|---|---|
| x + y = 7 | 4 + 3 = 7 |
| x − y = 1 | 4 − 3 = 1 |
One worked example
- x + y = 7; x − y = 1Two different conditions on the same x and y.
- 2x = 8 → x = 4Add corresponding sides: +y and −y cancel.
- 4 + y = 7 → y = 3Put x into an original equation, then check both equations.
Watch out: A system need not have exactly one solution. Distinct parallel lines never meet; identical lines have infinitely many common points.
Goal, prerequisites and card origin
What you will learn: Solve two linear equations by elimination and check both.
What you need first: Linear equations, negative numbers and point coordinates.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
OpenStax: solving systems by elimination ↗Show connections
A solution must satisfy both equations at once. Adding suitable equations can remove one unknown.