How it works

Simultaneous equations have two unknowns and are solved using two equations at once. The elimination method multiplies equations so that one variable's coefficients match, then adds or subtracts to remove it. The substitution method rearranges one equation and substitutes it into the other. Both methods find the point where two lines intersect.

The method

1. 1.Make the coefficients of one variable equal in both equations
2. 2.Add or subtract the equations to eliminate that variable
3. 3.Solve the resulting equation for the remaining variable
4. 4.Substitute back to find the other variable
5. 5.Check both values in the original equations

Worked example

Solve 2x + y = 11 and x - y = 1.

1. Add the equations: 3x = 12y terms cancel
2. x = 4
3. Substitute: 4 - y = 1, so y = 3

Worked example

Solve 3x + 2y = 16 and x + y = 6.

1. Multiply second equation by 2: 2x + 2y = 12
2. Subtract: x = 4
3. Substitute: y = 2

Common mistakes

• Adding equations when they should be subtracted (or vice versa)
• Forgetting to multiply every term in an equation when scaling it
• Substituting the found value into the original equation incorrectly to find the second unknown