Question

How do you solve the system of equations `2a - 5b = - 19` and `3a + 5b = 9`?

Answer 1

`a=-2` and `b=3`.

Explanation:

We have two equations `2a-5b=-19` and `3a+5b=9`.

It is noted that coefficients of `b` in the equations add up to `0` and hence adding the two equations we get

`2a-5b+3a+5b=-19+9` or

`2a-cancel(5b)+3a+cancel(5b)=-19+9` or

`5a=-10` or `a=-10/5=-2`

Substituting `a` in first equation, we get

`2xx(-2)-5b=-19` or

`-4-5b=-19` or

`-5b=-19+4=-15` and

`b=(-15)/(-5)=3`

Hence `a=-2` and `b=3`.

Answer 2

`a=-2, b=3`

Explanation:

In a system of equations, we can have the two equations interact and there are a couple of ways to do this in this question. I'm going to add the one equation to the other:

`2a-5b=-19`
`3a+5b=9`

`5a=-10`

`a=-2`

Which means that:

`2a-5b=-19`

`2(-2)-5b=-19`

`-4-5b=-19`

`5b=15`

`b=3`

The other way I could have started was by solving each equation for 5b, then setting them equal to each other:

`2a-5b=-19`

`5b=2a+19`

and

`3a+5b=9`

`5b=-3a+9`

and so

`2a+19=-3a+9`

`5a=-10`

`a=-2`