This is where you are given 2 different equations with 2 different variables:
(1) x - y = 5
(2) x + 2y = 11
Ok, so where do we start? Actually, there are 2 ways - and you need to be able to do both, because sometimes one of them won't work!
1: The elimination method
First of all, we subtract eqation 2 from equation 1. We can ONLY use this method where we have the SAME quantity of the SAME variable - in this case, x. Because subtracting x from x would eliminate x and get us a step closer to finding y.
Doing this gives:
- 3y = -6
This turns into:
3y = 6
And then:
y = 2
Knowing that y is 2, we can now find x by rearranging one equation to make x the subject of it.
x - y = 5
=
x = 5 + y
We can now subsitute y = 2 to make:
x = 5 + 2
=
x = 7
So x = 7 and y = 2.
2: The subsitution method
Ok, first we do what we did before, and make x the subject of equation 1.
x = 5 + y
Now we substitute THIS into quation 2:
(5 + y) + 2y = 11
There is nothing in front of the brackets, so we can just get rid of them:
5 + y + 2y = 11
This simplifies to:
5 + 3y =11
And we can then rearrange it to make:
3y = 6
=
y = 2
Then we substitute y = 2 into equation 2 like before.
x = 5 + 2
=
x = 7
Remember, both methods might not always work, so you need to know both of them!
And don't worry if you don't get it at first. Just keep practicing. Here is a short quiz to test yourself:
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