Let’s look at an example of solving simultaneous equations using the elimination method. The two equations are:

- 5x + y = 12
- 3x + 2y = 10

We can make one of the two pronumerals – x or y’s coefficient – equal by one of two ways –

- multiplying equation 1 by 2, and subtracting equation 2 from 1, i.e. 1.x2 – 2., or
- multiplying equation 2 by 5 and subtracting equation 1 multiplied by 3 i.e. 1.x3 – 2.x5

Multiplying equation 1 by 2 and subtracting the second equation (i.e. 1. x 2 − 2.), we get

10x | + | 2y | = | 24 | – |

3x | + | 2y | = | 10 | |

7x | + | 0 | = | 14 |

7x = 14

x = 2

Put x = 2 in equation 1 –

5x + y = 12

5×2 + y = 12

y = 12 – 10

y = 2, and x = 2

Check x = 2, and y = 2 in both the equations –

- 5×2 + 2 = 12
- 3×2 + 2×2 = 10

Both answers are correct, so x = 2, and y = 2 is the solution, usually given as co-ordinates (2, 2).