# How do you solve y=x-1 and y=-2x+5 using substitution?

Jan 24, 2017

You can set both equations equal to each other.

#### Explanation:

It is difficult to solve equations with multiple variables. To eliminate these variables, we solve for one variable and set the equations equal to each other.

In this case, both equations equal y, so we can say that both equations equal each other.

$x - 1 = - 2 x + 5$

Then, we can use simply isolate the variable and solve for x.
To start, we will add 1 to both sides.

$x - 1 + 1 = - 2 x + 5 + 1$

This simplifies to the following.

$x = - 2 x + 6$

To further isolate the variable, we must add 2x to both sides.
This becomes the following.

$3 x = 6$

Dividing both sides by 3 gives us the following.

$x = 2$

Now, solving for y is easy. We simply plug 2 into the first equation whenever we see x and solve for y.

$y = x - 1$
$y = 2 - 1$
$y - 1$