# Question #1847b

Oct 2, 2015

First number is -10
Second number is -8

#### Explanation:

Let $x$ be the first number.
Let $y$ be the second number.

First Equation:
The first number is 2 less than the second number.
$\textcolor{b l u e}{x = y - 2}$

Second Equation:
Twice the first number is 4 more than 3 times the second.
$\textcolor{red}{2 x = 4 + 3 y}$

System:
$\textcolor{b l u e}{x = y - 2}$
$\textcolor{red}{2 x = 4 + 3 y}$

We can solve this by substitution. Let's get the value of $x$ in the first equation and substitute it into $x$ in the second equation. Then, we can solve for $y$.

$2 \textcolor{b l u e}{x} = 4 + 3 y$
$2 \textcolor{b l u e}{\left(y - 2\right)} = 4 + 3 y$
$2 y - 4 = 4 + 3 y$
$2 y - 4 - 3 y = 4 + 3 y - 3 y$
$- 4 - y = 4$
$- 4 - y + 4 = 4 + 4$
$- y = 8$
$\textcolor{m a \ge n t a}{y = - 8}$

To solve for $x$, just substitute the value of $y$ into either of the two equations.
$x = \textcolor{m a \ge n t a}{y} - 2$
$x = \textcolor{m a \ge n t a}{\left(- 8\right)} - 2$
$\textcolor{\mathmr{and} a n \ge}{x = - 10}$