What is the solution (a, c) to this system of linear equations?

2a – 3c = –6

a + 2c = 11

Method:

Simultaneous equations

Explanation:

First we will need to get both equations to have the same subject, to do this we will multiply the bottom equation by 2.

1) 2a-3c=-6

2) a+2c=11 x2
Becomes
2) 2a+4c=22

Now we will make both equations equal to the same subject (2a)

1) 2a=3c-6
2) 2a=-4c+22

Because they are both equal to 2a, they are therefore equal to each other, so:

3c-6=-4c+22
7c=28
c=4

Now substitute c back into either equation to get a:

a+2c=11
a+2(4)=11
a=3