Graph x+2y=-5 and -2x+y=3

$x + 2 y = - 5$ and $- 2 x + y = 3$

Step 1

Graph $x + 2 y = - 5$ .

Solve for $y$ .

Subtract $x$ from both sides of the equation.

$2 y = - 5 - x$

Divide each term in $2 y = - 5 - x$ by $2$ and simplify.

Divide each term in $2 y = - 5 - x$ by $2$ .

$\frac{2 y}{2} = \frac{- 5}{2} + \frac{- x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 5}{2} + \frac{- x}{2}$

Divide $y$ by $1$ .

$y = \frac{- 5}{2} + \frac{- x}{2}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{5}{2} + \frac{- x}{2}$

Move the negative in front of the fraction.

$y = - \frac{5}{2} - \frac{x}{2}$

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 $- \frac{5}{2}$ and $- \frac{x}{2}$ .

$y = - \frac{x}{2} - \frac{5}{2}$

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

Reorder terms.

$y = - (\frac{1}{2} x) - \frac{5}{2}$

Remove parentheses.

$y = - \frac{1}{2} x - \frac{5}{2}$

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

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

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

$b = - \frac{5}{2}$

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: $(0, - \frac{5}{2})$

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

y-intercept: $(0, - \frac{5}{2})$

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 $- \frac{5}{2}$ and $- \frac{x}{2}$ .

$y = - \frac{x}{2} - \frac{5}{2}$

Reorder terms.

$y = - (\frac{1}{2} x) - \frac{5}{2}$

Remove parentheses.

$y = - \frac{1}{2} x - \frac{5}{2}$

Find the x-intercept.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = - \frac{1}{2} x - \frac{5}{2}$

Solve the equation.

Rewrite the equation as $- \frac{1}{2} x - \frac{5}{2} = 0$ .

$- \frac{1}{2} x - \frac{5}{2} = 0$

Combine $x$ and $\frac{1}{2}$ .

$- \frac{x}{2} - \frac{5}{2} = 0$

Add $\frac{5}{2}$ to both sides of the equation.

$- \frac{x}{2} = \frac{5}{2}$

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- x = 5$

Divide each term in $- x = 5$ by $- 1$ and simplify.

Divide each term in $- x = 5$ by $- 1$ .

$\frac{- x}{- 1} = \frac{5}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{5}{- 1}$

Divide $x$ by $1$ .

$x = \frac{5}{- 1}$

Simplify the right side.

Divide $5$ by $- 1$ .

$x = - 5$

x-intercept(s) in point form.

x-intercept(s): $(- 5, 0)$

Find the y-intercept.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = - \frac{1}{2} \cdot 0 - \frac{5}{2}$

Solve the equation.

Remove parentheses.

$y = - \frac{1}{2} \cdot 0 - \frac{5}{2}$

Simplify $- \frac{1}{2} \cdot 0 - \frac{5}{2}$ .

Multiply $- \frac{1}{2} \cdot 0$ .

Multiply $0$ by $- 1$ .

$y = 0 (\frac{1}{2}) - \frac{5}{2}$

Multiply $0$ by $\frac{1}{2}$ .

$y = 0 - \frac{5}{2}$

Subtract $\frac{5}{2}$ from $0$ .

$y = - \frac{5}{2}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{5}{2})$

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

$\begin{array}{c} x & y \\ - 5 & 0 \\ 0 & - \frac{5}{2} \end{array}$

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

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

y-intercept: $(0, - \frac{5}{2})$

$\begin{array}{c} x & y \\ - 5 & 0 \\ 0 & - \frac{5}{2} \end{array}$

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

y-intercept: $(0, - \frac{5}{2})$

$\begin{array}{c} x & y \\ - 5 & 0 \\ 0 & - \frac{5}{2} \end{array}$

Step 2

Graph $- 2 x + y = 3$ .

Add $2 x$ to both sides of the equation.

$y = 3 + 2 x$

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 $2 x$ .

$y = 2 x + 3$

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

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

$m = 2$

$b = 3$

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

Slope: $2$

y-intercept: $(0, 3)$

Slope: $2$

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.

Reorder $3$ and $2 x$ .

$y = 2 x + 3$

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

$\begin{array}{c} x & y \\ 0 & 3 \\ 1 & 5 \end{array}$

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

Slope: $2$

y-intercept: $(0, 3)$

$\begin{array}{c} x & y \\ 0 & 3 \\ 1 & 5 \end{array}$

Slope: $2$

y-intercept: $(0, 3)$

$\begin{array}{c} x & y \\ 0 & 3 \\ 1 & 5 \end{array}$

Step 3

Plot each graph on the same coordinate system.

$x + 2 y = - 5$

$- 2 x + y = 3$

Step 4

Graph x+2y=-5 and -2x+y=3

Related Questions

Support LCMGCF.com by disabling your adblocker.