Solve by Graphing x-2y=5 , x+2y=-1

$x - 2 y = 5$ , $x + 2 y = - 1$

Step 1

Subtract $x$ from both sides of the equation.

$- 2 y = 5 - x$

$x + 2 y = - 1$

Step 2

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

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

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

$x + 2 y = - 1$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

$x + 2 y = - 1$

Divide $y$ by $1$ .

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

$x + 2 y = - 1$

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

$x + 2 y = - 1$

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

$x + 2 y = - 1$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

$x + 2 y = - 1$

Dividing two negative values results in a positive value.

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

$x + 2 y = - 1$

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

$x + 2 y = - 1$

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

$x + 2 y = - 1$

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

$x + 2 y = - 1$

Step 3

Subtract $x$ from both sides of the equation.

$2 y = - 1 - x$

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

Step 4

Divide each term in $2 y = - 1 - x$ by $2$ and simplify.

Divide each term in $2 y = - 1 - x$ by $2$ .

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

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

Divide $y$ by $1$ .

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

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

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

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

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

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

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

Move the negative in front of the fraction.

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

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

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

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

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

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

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

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

Step 5

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.

$(2, - \frac{3}{2})$

Step 6

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