How do you solve a simultaneous equation?

Example question:

Solving Simultaneous Equations

Equation 1: 6x + 2y = 2
Equation 2: 5x - 7y = 6.
Find x and y.

1) Check is if it is possible to solve. Here we have 2 unknowns, x and y, and 2 equations, therefore it is possible to solve. (If there are more unknowns than equations then it is not possible to solve.)

2) Eliminate an unknown in one of the equations.

- Rearrange each equation to get the x terms on one side and the y terms on the other.

Eq 1 .... 6x=2-2y
Eq 2 .... 5x=6+7y

- Look for a common multiple for the coefficients (number in front of the unknown) of x, e.g. 30. So we multiply each equation up to get 30x on one side, then we can say equation 1 equals equation 2.

5 x Eq 1 .... 30x=10-10y .... we will call this Eq 3
6 x Eq 2 .... 30x=36+42y .... we will call this Eq 4

- Remember what you do to one side of the equation you must do to the other.

3) Now both Eq3 and Eq4 are of the form 30x=.... we can say that Eq3=Eq4.

10-10y = 36+42y

4) Now just solve as you would normally to find y=-0.5.

5) Put this value of y into Eq1 to find x=0.5.

6) Put both these values into Eq2 to check result, e.g. 60.5 + 2-0.5 = 3 - 1 = 2.
This is correct therefore we have the correct answer.