# Question #15aab

Nov 21, 2016

$p = 3 \text{ and } q = 4$

#### Explanation:

The question to be solved is.

$5 p - 7 q = - 13 \to \left(1\right)$
$2 p + 7 q = 34 \to \left(2\right)$

The aim here is to eliminate one of the variables from the equations by performing operations on them. We then have a one variable equation which we can solve. Then substitute this value into either one of the 2 given equations and solve for the other variable.

I have labelled the equations to assist.

Note that in (1) there is a - 7q and in (2) there is + 7q

Adding these together will eliminate the variable q, which is what we want.

Add (1) and (2) together term by term on both sides.

$\Rightarrow 7 p + 0 = 21 \Rightarrow 7 p = 21 \Rightarrow p = 3$

Now substitute p = 3 into (1) or (2). I'll choose (2) you can perhaps try (1).

$\Rightarrow \left(2 \times 3\right) + 7 q = 34$

$\Rightarrow 6 + 7 q = 34 \Rightarrow 7 q = 28 \Rightarrow q = 4$

Hope this helps.