Add or subtract the equations to remove one letter, multiplying first when the numbers do not match.
What you will learn
- Add or subtract equations to eliminate a letter
- Multiply one or both equations first
- Substitute back and check in both equations
Make one letter disappear
Two equations, two unknowns.
If the y terms match, adding or subtracting the equations removes y.
- 3x + 2y = 16
- 5x − 2y = 0
- add: 8x = 16, so x = 2
- substitute: 3 × 2 + 2y = 16, so y = 5
- check in the second: 5 × 2 − 2 × 5 = 0
Same signs: subtract. Opposite signs: add. You can remove either letter: in 2x + y = 11 and 2x − 3y = −1 the x terms match, so subtract to get 4y = 12. Then y = 3, and 2x + 3 = 11 gives x = 4.
To check a pair of values, substitute them into both equations. x = 2, y = 5 fits 3x + 2y = 16 and 5x − 2y = 0, so it is the solution; a pair that fits only one equation is not.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Make one letter disappear
- When the numbers do not match
- Try it: Check with the solver
7 practice questions, marked as you go; about 25 minutes in all.
In this unit: Simultaneous equations
Solve two equations at once by elimination, substitution and graphs, form them from problems, and (Higher) solve a linear and a quadratic equation together.