What are linear simultaneous equations?
When there are two unknowns (say x and y) in a problem, we need two equations to be able to find them both. These are called Simultaneous Equations.
If they just have x and y in them (no x2 or y2) then they are Linear Simultaneous Equations. (They can be represented by two straight lines on a graph – the two answers are the x and y coordinates of the point of intersection of the lines.)
The method described here is called the Elimination (or Balance) Method:
Label the equations A and B
- Multiply A and/or B by numbers to make the coefficients of x or y the same size.
- Add or subtract appropriate equations to eliminate that variable.
(Note: if the coefficients you made the same size in 1. have different signs you will be adding. If they have the same signs you will be subtracting.)
- Solve the resulting equation.
- Substitute back into A or B and solve to find the other variable.
- Check your answer by substituting into the equation you didn’t use in 4.