# How do you solve the system?: X+Y= -1, Y=3X-17

Mar 2, 2018

$X = 4 , Y = - 5$

#### Explanation:

If we know $Y = 3 X - 17 ,$ we can just go ahead and replace $Y$ in $X + Y = - 1$ with $3 X - 17$

$X + Y = - 1 \Leftrightarrow X + 3 X - 17 = - 1$

Now, we have an equation with one unknown variable, which can be easily solved.

$4 X - 17 = - 1$

$4 X = - 1 + 17 = 16$

$X = \frac{16}{4} = 4$

We need $Y .$ We know $X = 4 ,$ so we can plug in $4$ for $X$ in $X + Y = - 1$ and solve for $Y :$

$4 + Y = - 1$

$Y = - 1 - 4 = - 5$