Graph x+2y=6 x-y=3

$x + 2 y = 6$ $x - y = 3$

Step 1

Graph $x + 2 y = 6$ .

Solve for $y$ .

Subtract $x$ from both sides of the equation.

$2 y = 6 - x$

Divide each term in $2 y = 6 - x$ by $2$ and simplify.

Divide each term in $2 y = 6 - x$ by $2$ .

$\frac{2 y}{2} = \frac{6}{2} + \frac{- x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{6}{2} + \frac{- x}{2}$

Divide $y$ by $1$ .

$y = \frac{6}{2} + \frac{- x}{2}$

Simplify the right side.

Simplify each term.

Divide $6$ by $2$ .

$y = 3 + \frac{- x}{2}$

Move the negative in front of the fraction.

$y = 3 - \frac{x}{2}$

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 $- \frac{x}{2}$ .

$y = - \frac{x}{2} + 3$

Write in $y = m x + b$ form.

Reorder terms.

$y = - (\frac{1}{2} x) + 3$

Remove parentheses.

$y = - \frac{1}{2} x + 3$

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

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

$m = - \frac{1}{2}$

$b = 3$

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

Slope: $- \frac{1}{2}$

y-intercept: $(0, 3)$

Slope: $- \frac{1}{2}$

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.

Write in $y = m x + b$ form.

Reorder $3$ and $- \frac{x}{2}$ .

$y = - \frac{x}{2} + 3$

Reorder terms.

$y = - (\frac{1}{2} x) + 3$

Remove parentheses.

$y = - \frac{1}{2} x + 3$

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

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

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

Slope: $- \frac{1}{2}$

y-intercept: $(0, 3)$

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

Slope: $- \frac{1}{2}$

y-intercept: $(0, 3)$

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

Step 2

Graph $x - y = 3$ .

Solve for $y$ .

Subtract $x$ from both sides of the equation.

$- y = 3 - x$

Divide each term in $- y = 3 - x$ by $- 1$ and simplify.

Divide each term in $- y = 3 - x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{3}{- 1} + \frac{- x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{3}{- 1} + \frac{- x}{- 1}$

Divide $y$ by $1$ .

$y = \frac{3}{- 1} + \frac{- x}{- 1}$

Simplify the right side.

Simplify each term.

Divide $3$ by $- 1$ .

$y = - 3 + \frac{- x}{- 1}$

Dividing two negative values results in a positive value.

$y = - 3 + \frac{x}{1}$

Divide $x$ by $1$ .

$y = - 3 + x$

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 3

Plot each graph on the same coordinate system.

$x + 2 y = 6$

$x - y = 3$

Step 4

Graph x+2y=6 x-y=3

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