Solve by Graphing x+y=3 x-2y=1

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

Step 1

Subtract $x$ from both sides of the equation.

$y = 3 - x$

$x - 2 y = 1$

Step 2

Subtract $x$ from both sides of the equation.

$- 2 y = 1 - x$

$y = 3 - x$

Step 3

Divide each term in $- 2 y = 1 - x$ by $- 2$ and simplify.

Divide each term in $- 2 y = 1 - x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{1}{- 2} + \frac{- x}{- 2}$

$y = 3 - x$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{1}{- 2} + \frac{- x}{- 2}$

$y = 3 - x$

Divide $y$ by $1$ .

$y = \frac{1}{- 2} + \frac{- x}{- 2}$

$y = 3 - x$

$y = \frac{1}{- 2} + \frac{- x}{- 2}$

$y = 3 - x$

$y = \frac{1}{- 2} + \frac{- x}{- 2}$

$y = 3 - x$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{1}{2} + \frac{- x}{- 2}$

$y = 3 - x$

Dividing two negative values results in a positive value.

$y = - \frac{1}{2} + \frac{x}{2}$

$y = 3 - x$

$y = - \frac{1}{2} + \frac{x}{2}$

$y = 3 - x$

$y = - \frac{1}{2} + \frac{x}{2}$

$y = 3 - x$

$y = - \frac{1}{2} + \frac{x}{2}$

$y = 3 - x$

Step 4

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.

$(\frac{7}{3}, \frac{2}{3})$

Step 5