# How do you solve the system y=x-1 and x+y =3?

Mar 3, 2018

Since only one of the variables is defined, we can use the substitution method so first, substitute for y
$x + \left(x - 1\right) = 3$

Then, combine like terms and solve for x
$2 x - 1 = 3$
$x = 2$

Now that we know what x is, we can substitute for x in the other equation to find y
$y = 2 - 1$
$y = 1$

Now that we know what both x and y are, we can substitute for the variables
$1 = 2 - 1$ (correct)
$2 + 1 = 3$ (correct)

We can now conclude the answer
$\left(2 , 1\right)$