Graph 3x+5y<=10 x-y<-1

$3 x + 5 y \leq 10$ $x - y < - 1$

Step 1

Graph $3 x + 5 y \leq 10$ .

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

Solve for $y$ .

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

$5 y \leq 10 - 3 x$

Divide each term in $5 y \leq 10 - 3 x$ by $5$ and simplify.

Divide each term in $5 y \leq 10 - 3 x$ by $5$ .

$\frac{5 y}{5} \leq \frac{10}{5} + \frac{- 3 x}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} \leq \frac{10}{5} + \frac{- 3 x}{5}$

Divide $y$ by $1$ .

$y \leq \frac{10}{5} + \frac{- 3 x}{5}$

Simplify the right side.

Simplify each term.

Divide $10$ by $5$ .

$y \leq 2 + \frac{- 3 x}{5}$

Move the negative in front of the fraction.

$y \leq 2 - \frac{3 x}{5}$

Rearrange terms.

$y \leq - \frac{3 x}{5} + 2$

Reorder terms.

$y \leq - (\frac{3}{5} x) + 2$

Remove parentheses.

$y \leq - \frac{3}{5} x + 2$

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

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

$m = - \frac{3}{5}$

$b = 2$

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

Slope: $- \frac{3}{5}$

y-intercept: $(0, 2)$

Slope: $- \frac{3}{5}$

y-intercept: $(0, 2)$

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- \frac{3}{5} x + 2$ .

$y \leq - \frac{3}{5} x + 2$

Step 2

Graph $x - y < - 1$ .

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

Solve for $y$ .

Subtract $x$ from both sides of the inequality.

$- y < - 1 - x$

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

Divide each term in $- y < - 1 - x$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

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 $1$ .

$y > 1 + x$

Rearrange terms.

$y > x + 1$

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 $y = m x + b$ .

$m = 1$

$b = 1$

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: $(0, 1)$

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $x + 1$ .

$y > x + 1$

Step 3

Plot each graph on the same coordinate system.

$3 x + 5 y \leq 10$

$x - y < - 1$

Step 4

Graph 3x+5y<=10 x-y<-1

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