# How do you solve the system of equations: y = 3x - 4 and 2x - y = 1?

Sep 17, 2015

I found:
$x = 3$
$y = 5$

#### Explanation:

You can substitute the value of $y$ from the first equation into the second and solve for $x$ as:
$2 x - \textcolor{red}{\left[3 x - 4\right]} = 1$
$2 x - 3 x + 4 = 1$
$- x = - 3$
$x = 3$
substitute back this value into the first equation to find $y$:
$y = 3 \cdot \left(3\right) - 4 = 5$

Refer to explanation

#### Explanation:

We have two equations

$y = 3 x - 4$ and $y = 2 x - 1$ Multiply the first with 2 and the second with three and substract them

$2 y - 3 y = 2 \cdot \left(3 x - 4\right) - 3 \left(2 x - 1\right) \implies - y = - 5 \implies y = 5$ and $x = 3$