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Study Guide : Simultaneous Equations

Learner Guide


Simultaneous Equations

L . O to be able to solve equations with 2 different variables

by satisfying both equations in the problem.

When we looked at Linear Equations on the previous Online Algebra

Help page we were simply working out the value of the term in the problem.

Notice they were all something like 4p + 10 = 5p – 2 both containing “p” so

we could easily solve  the problem. What if you received a problem like

4x + y = 15 & 2x + 3y = 10 .


How would you tackle this when you would still have the variables “x” and

“y” left at the end? This is where our Tutors are ready to help using 

simultaneous equations.


Example 1

Solve the simultaneous equations.

4x + y = 15

x + y = 8




Step 1: Label each equation 1 and 2.


Step 2: Eliminate one of the variables. If you see one of the variables x or y are the same, then you can apply a simple addition or subtraction to the equations to remove it.


Step 3: Here in Equation 1 and Equation 2 you have “y” in each one. To remove “y” all you need to do is subtract.


Step 4: Now substitute the value of “x” you calculated and rearrange the equation so you work out the value of y. (Any problems look at the Linear Equations sheet).


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Related Topics

Patterns-and-sequences                                            changing-the-formulae

Adding-subtracting-formulas                                   Algebraic-proof



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