Foundation and Higher · two equations

Simultaneous
equations.
Eliminate a letter.

two equations,
two unknowns

the word itself —

Simultaneous

at the same time

one x and one y that fit both equations

step 1 of 4

Eliminate

1. Both have 2y. Subtract and it disappears.

2. 3x − x = 2x, and 16 − 8 = 8.

✓ Same signs: subtract

3x + 2y = 16 (1)

  x + 2y = 8 (2)

2x = 8 (1) − (2)

x = 4

step 2 of 4

Substitute back

1. Put x = 4 into either equation.

2. Solve it for y.

✓ Check in (1): 3 × 4 + 2 × 2 = 16

x + 2y = 8 use (2)

4 + 2y = 8

2y = 4

x = 4, y = 2

step 3 of 4

Nothing matches?

1. Multiply (1) by 2 so both have 2y.

2. Subtract: 4x − 3x = x, 14 − 12 = 2.

✓ Multiply every term, both sides

2x + y = 7 (1)

3x + 2y = 12 (2)

4x + 2y = 14 (1) × 2

x = 2 subtract (2)

x = 2, y = 3

step 4 of 4

What it means

1. Each equation is a straight line.

2. The solution is where they cross.

✓ x = 2, y = 3 is the point (2, 3)

elimination —

Match

make one letter the same size

Eliminate

same signs: subtract

Substitute

to find the other letter

Different signs? Add instead.
Then check in the other equation.

The
Maths Habit

Download The Maths Habit app
to test your knowledge