How to solve simultaneous equations?

Several methods exist, for example:

Add one equation to the other equation - or add multiples of each equation.

Example:

x+y = 5

2x-y = 10

Adding the equations results in:

3x = 15

Now you can solve for x; this is then replaced in one of the original equations.

Solve one equation for one variable. Substitute in the other equation. Example:

x+y = 5

2x-y = 10

Solve the first equation for x: x = 5 - y

Replace in the second equation: 2(5-y) - y = 10

Once again, you can solve for one variable, then replace that variable in one of the original equations.

Solve both equations for the same variable.

Example:

x+y = 5

2x-y = 10

Solve each equation for x:

Equation 1: x = 5 - y

Equation 2: 2x = 10 - y; x = 5 - y/2

Equate the right sides of both equations (this is valid, since they are both equal to x):

5 - y = 5 - y/2