Simultaneous equations GCSE lesson: elimination and where two lines cross

Simultaneous equations: practice

Show your working on paper and check each pair in both equations. The stretch is optional.

Diagnostic question: choose and explain

1. Solve 3x + 2y = 16 and x − 2y = 0.
   1. x = 4, y = 2
   2. x = 8, y = −4
   3. x = 4, y = −2
   4. x = 8, y = 4

Practice questions

1. x + y = 8 and x − y = 2, so x = ___ and y = ___
2. 3x + y = 11 and x + y = 5, so x = ___ and y = ___
3. y = 2x + 1 and y = 7 − x, so x = ___ and y = ___
4. 2x + 3y = 13 and 2x + y = 7, so x = ___ and y = ___
5. The lines of two equations cross at (3, −1). What does that tell you?
   1. x = 3, y = −1 solves both equations
   2. x = −1, y = 3 solves both equations
   3. x = 3, y = −1 solves only one of them
6. y = 2x + 1 and y = 2x + 4. How many solutions does the pair have?
   1. None
   2. One
   3. Infinitely many
7. 3 pens and 2 rulers cost £3.10. 1 pen and 2 rulers cost £1.70. A pen costs £___
8. Stretch: y = x² and y = x + 2 meet at the smaller x = ___ and the larger x = ___

Support: For question 1: add the two equations, and y goes. Then put x back into x + y = 8 to find y. Check the pair in x − y = 2 too. When both equations say what y is (y = … and y = …), set the two right-hand sides equal.

Simultaneous equations: exit

Show your working; one sentence for the second part.

1. Solve x + y = 6 and y = x + 2. Then say in one sentence how a graph of the two lines would show your answer.

Exit check

One pair solved and one sentence show who links the answer to the crossing.

Solve x + y = 6 and y = x + 2 in any way: elimination, substitution or a sketch.

Simultaneous equations: solve and check

Solve each pair. For questions 1, 2, 3 and 5, write whether you add or subtract, and why. Check every pair in both equations. For question 6, sketch both lines and mark where they cross.