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