# When the expression x-1 is substituted into the first equation for y, what is the resulting equation when given 3x-y=2, y=x-1?

Nov 29, 2016

$x = \frac{3}{2}$
Every step shown. As you become more confident with this type of question you will start to jump steps and become much faster at solving them.

#### Explanation:

Given:

$\text{ "y=x-1" } \ldots \ldots \ldots \ldots \ldots \ldots . E q u a t i o n \left(1\right)$
$3 x - y = 2 \text{ } \ldots \ldots \ldots \ldots \ldots \ldots . . E q u a t i o n \left(2\right)$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Using equation(1) substitute for $y$ in equation(2)

color(green)(3xcolor(red)(-y)=2" "->" "3xcolor(red)(-(x-1))=2

$3 x - x + 1 = 2$

but $3 x - x = 2 x$

$2 x - 1 = 2$

$2 x - 1 + 1 = 2 + 1$

$2 x + 0 = 3$

$2 x = 3$

Divide both sides by 2

$\frac{2}{2} \times x = \frac{3}{2}$

But $\frac{2}{2} = 1$

$x = \frac{3}{2}$