Graph 6x+2y>14 3x+y<=3

$6 x + 2 y > 14$ $3 x + y \leq 3$

Graph $6 x + 2 y > 14$ .

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

Solve for $y$ .

Subtract $6 x$ from both sides of the inequality.

$2 y > 14 - 6 x$

Divide each term in $2 y > 14 - 6 x$ by $2$ and simplify.

Divide each term in $2 y > 14 - 6 x$ by $2$ .

$\frac{2 y}{2} > \frac{14}{2} + \frac{- 6 x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} > \frac{14}{2} + \frac{- 6 x}{2}$

Divide $y$ by $1$ .

$y > \frac{14}{2} + \frac{- 6 x}{2}$

Simplify the right side.

Simplify each term.

Divide $14$ by $2$ .

$y > 7 + \frac{- 6 x}{2}$

Cancel the common factor of $- 6$ and $2$ .

Factor $2$ out of $- 6 x$ .

$y > 7 + \frac{2 (- 3 x)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$y > 7 + \frac{2 (- 3 x)}{2 (1)}$

Cancel the common factor.

$y > 7 + \frac{2 (- 3 x)}{2 \cdot 1}$

Rewrite the expression.

$y > 7 + \frac{- 3 x}{1}$

Divide $- 3 x$ by $1$ .

$y > 7 - 3 x$

Rearrange terms.

$y > - 3 x + 7$

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

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

$y = m x + b$

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

$m = - 3$

$b = 7$

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

Slope: $- 3$

y-intercept: $(0, 7)$

Slope: $- 3$

y-intercept: $(0, 7)$

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $- 3 x + 7$ .

$y > - 3 x + 7$

Graph $3 x + y \leq 3$ .

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

Subtract $3 x$ from both sides of the inequality.

$y \leq 3 - 3 x$

Rearrange terms.

$y \leq - 3 x + 3$

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

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

$y = m x + b$

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

$m = - 3$

$b = 3$

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

Slope: $- 3$

y-intercept: $(0, 3)$

Slope: $- 3$

y-intercept: $(0, 3)$

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- 3 x + 3$ .

$y \leq - 3 x + 3$

Plot each graph on the same coordinate system.

$6 x + 2 y > 14$

$3 x + y \leq 3$

Graph 6x+2y>14 3x+y<=3

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