# Twice a number minus a second number is -1. Twice the second number added to three times the first number is 9. How do you find the two numbers?

Dec 6, 2016

The first number is $1$ and the second number is $3$.

#### Explanation:

We consider the first number as $x$ and the second as $y$. From the data, we can write two equations:

$2 x - y = - 1$
$3 x + 2 y = 9$

From the first equation, we derive a value for $y$.

$2 x - y = - 1$

Add $y$ to both sides.

$2 x = - 1 + y$

Add $1$ to both sides.

$2 x + 1 = y$ or $y = 2 x + 1$

In the second equation, substitute $y$ with $\textcolor{red}{\left(2 x + 1\right)}$.

$3 x + 2 \textcolor{red}{\left(2 x + 1\right)} = 9$

Open the brackets and simplify.

$3 x + 4 x + 2 = 9$

$7 x + 2 = 9$

Subtract $2$ from both sides.

$7 x = 7$

Divide both sides by $7$.

$x = 1$

In the first equation, substitute $x$ with $\textcolor{red}{1}$.

$\left(2 \times \textcolor{red}{1}\right) - y = - 1$

$2 - y = - 1$

Add $y$ to both sides.

$2 = y - 1$

Add $1$ to both sides.

$3 = y$ or $y = 3$