How can I solve simultaneous equations?

We can solve simultaneous equations in two different ways. We can either eliminate one of the unknowns or use substitution. It is about finding which method you are most comfortable with and practicing that method. We will first look at the method of elimination.

If I am given the two equations:

2x + y = 7

3x - y = 8 

To begin I would add the two equations to get rid of the y. So 

2x + y = 7


3x - y = 8

would become: 5x = 15

(if the equations had two positive y's we would then subtract the equations to get rid of the y.)

With the 5x = 15 we can get what value x would have by dividing 15 by 5.

Then x = 3.

Since we know that x = 3 all we have to do is put 3 back into one of the original equations to find out what y is. 

so 2x + y = 7 would become (2x3) + y =7 which is 6+y= 7

y=7-6 so y=1.

The answers are then x=3 and y=1. 

We will now look at the method of substitution.

If we are given the equations of:

y - 2x = 1

2y -3x = 5

We can rearrange y - 2x =1 to become 


We can then substitute y into the other equation so 

2(1+2x) - 3x = 5

2 + 4x -3x = 5

2 + x = 5

x= 5-2


Now that we know what x is we can substitute it into one of equations to find out what y is

so y-2x=1

y- (2x3) =1


y= 1+6


So the answer is x=3 and y=7

SImultaneous equations can look difficult but after some practice and finding out what method you prefer you will be able to solve them!

Meabh M. GCSE Maths tutor, GCSE English tutor, GCSE History tutor

11 months ago

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