Simultaneous equations are two equations that are both true for the same x and y. With x + y = 9 and x − y = −1, adding the equations removes y: 2x = 8, so x = 4. Then 4 + y = 9 gives y = 5.
This is the elimination method. If neither letter cancels straight away, multiply one or both equations first so that one letter has the same coefficient. On a graph, the solution is where the two straight lines cross.
Worked example
Solve x + 2y = 12 and −x + 2y = 8
- Add the equations: 4y = 20, so y = 5.
- Substitute: x + 10 = 12, so x = 2.
Answer:x = 2, y = 5
Key words
- simultaneous
- true at the same time
- eliminate
- remove one unknown by adding or subtracting
- substitute
- put a value back into an equation
Practise this
New questions every time.
Common Core-referenced: 8.EE.C.8