Graph x+y=3 x-y=1

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

Step 1

Graph $x + y = 3$ .

Subtract $x$ from both sides of the equation.

$y = 3 - x$

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Reorder $3$ and $- x$ .

$y = - x + 3$

Use the slope-intercept form to find the slope and y-intercept.

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = - 1$

$b = 3$

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $- 1$

y-intercept: $(0, 3)$

Slope: $- 1$

y-intercept: $(0, 3)$

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

Reorder $3$ and $- x$ .

$y = - x + 3$

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & 3 \\ 1 & 2 \end{array}$

Graph the line using the slope and the y-intercept, or the points.

Slope: $- 1$

y-intercept: $(0, 3)$

$\begin{array}{c} x & y \\ 0 & 3 \\ 1 & 2 \end{array}$

Slope: $- 1$

y-intercept: $(0, 3)$

$\begin{array}{c} x & y \\ 0 & 3 \\ 1 & 2 \end{array}$

Step 2

Graph $x - y = 1$ .

Solve for $y$ .

Subtract $x$ from both sides of the equation.

$- y = 1 - x$

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

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

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $1$ by $- 1$ .

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

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

$y = - 1 + x$

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Reorder $- 1$ and $x$ .

$y = x - 1$

Use the slope-intercept form to find the slope and y-intercept.

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = 1$

$b = - 1$

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $1$

y-intercept: $(0, - 1)$

Slope: $1$

y-intercept: $(0, - 1)$

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

Reorder $- 1$ and $x$ .

$y = x - 1$

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & - 1 \\ 1 & 0 \end{array}$

Graph the line using the slope and the y-intercept, or the points.

Slope: $1$

y-intercept: $(0, - 1)$

$\begin{array}{c} x & y \\ 0 & - 1 \\ 1 & 0 \end{array}$

Slope: $1$

y-intercept: $(0, - 1)$

$\begin{array}{c} x & y \\ 0 & - 1 \\ 1 & 0 \end{array}$

Step 3

Plot each graph on the same coordinate system.

$x + y = 3$

$x - y = 1$

Step 4

Graph x+y=3 x-y=1

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