# Two times a number added to another number is 25. Three times the first number minus the other number is 20. How do you find the numbers?

$\left(x , y\right) = \left(9 , 7\right)$

#### Explanation:

We have two numbers, $x , y$. We know two things about them:

$2 x + y = 25$

$3 x - y = 20$

Let's add these two equations together which will cancel the $y$:

$5 x + 0 y = 45$

$x = \frac{45}{5} = 9$

We can now substitute in the $x$ value into one of the original equations (I'll do both) to get to $y$:

$2 x + y = 25$

$2 \left(9\right) + y = 25$

$18 + y = 25$

$y = 7$

$3 x - y = 20$

$3 \left(9\right) - y = 20$

$27 - y = 20$

$y = 7$