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)

• You may have to use the information in the question to write down the equations
• • For example, if the question says:“The cost of 5 apples and 3 bananas is $1.35”then you can write down the equation: 5a + 3b = 135where a is the cost of an apple in cents (and b is the cost of a banana in cents)

    Look for an “is” (or equivalent) in the question and make sure you know what the letters you are using stand for

How do you solve linear simultaneous equations?

• The method described here is called the Elimination (or Balance) Method:Label?the equations?A?and?B

1. Multiply A?and/or?B?by numbers to make the coefficients of x or y the same size
2. 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.)
3. Solve?the resulting equation
4. Substitute?back into?A?or?B?and solve to find the other variable
5. Check?your answer by substituting into the equation you didn’t use in 4