# How do you solve x+2y=3 and 3x-y= -5?

Aug 5, 2015

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

#### Explanation:

One way is to use the method of substitution.

Step 1. Enter the equations.

[1] $x + 2 y = 3$
[2] $3 x - y = - 5$

Step 2. Solve for one variable in terms of the other.

Solve Equation 2 for $y$.

[3] $y = 3 x + 5$

Step 3. Substitute Equation 3 in Equation 1 and solve for $x$.

$x + 2 \left(3 x + 5\right) = 3$

$x + 6 x + 10 = 3$

$7 x = - 7$

[4] $x = - 1$

Step 4. Substitute Equation 4 in Equation 1:

$- 1 + 2 y = 3$

$2 y = 4$

$y = 2$

The solution is $x = - 1 , y = 2$.

Check:

Substitute the values in Equation 2.

$3 x - y = - 5$

$3 \left(- 1\right) - 2 = - 5$

$- 3 - 2 = - 5$

$5 = 5$

It works!