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

Aug 3, 2015

I found:
$x = 1$
$y = 2$

#### Explanation:

I would isolate $x$ from the second equation and substitute it into the first:
$x = 3 - y$
into the first:
$3 \left(\textcolor{red}{3 - y}\right) - y = 1$
$9 - 3 y - y = 1$
$- 4 y = - 8$
$y = 2$
substitute this back into the second equation:
$x = 3 - 2 = 1$

Aug 3, 2015

$\textcolor{red}{x = 1 , y = 2}$

#### Explanation:

Gió's method uses the method of substitution.

Here's how to do it by the method of elimination.

Step 1. Enter the equations.

[1] $3 x - y = 1$
[2] $x + y = 3$

Step 2. Add Equations 1 and 2.**

$4 x = 4$

[3] $x = 1$

Step 3. Substitute Equation 3 in Equation 2.

$x + y = 3$
$1 + y = 3$

$y = 2$

Solution: $x = 1 , y = 2$

Check: Substitute the values of $x$ and $y$ in Equation 1.

$3 x - y = 1$
$3 \left(1\right) - 2 = 1$
$3 - 2 = 1$
$1 = 1$

It checks!

The solution is correct.