Solve by Graphing 5x+2y=2 , 3x-3y=18

$5 x + 2 y = 2$ , $3 x - 3 y = 18$

Step 1

Subtract $5 x$ from both sides of the equation.

$2 y = 2 - 5 x$

$3 x - 3 y = 18$

Step 2

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

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

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

$3 x - 3 y = 18$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

$3 x - 3 y = 18$

Divide $y$ by $1$ .

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

$3 x - 3 y = 18$

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

$3 x - 3 y = 18$

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

$3 x - 3 y = 18$

Simplify the right side.

Simplify each term.

Divide $2$ by $2$ .

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

$3 x - 3 y = 18$

Move the negative in front of the fraction.

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

$3 x - 3 y = 18$

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

$3 x - 3 y = 18$

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

$3 x - 3 y = 18$

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

$3 x - 3 y = 18$

Step 3

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

$- 3 y = 18 - 3 x$

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

Step 4

Divide each term in $- 3 y = 18 - 3 x$ by $- 3$ and simplify.

Divide each term in $- 3 y = 18 - 3 x$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{18}{- 3} + \frac{- 3 x}{- 3}$

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{18}{- 3} + \frac{- 3 x}{- 3}$

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

Divide $y$ by $1$ .

$y = \frac{18}{- 3} + \frac{- 3 x}{- 3}$

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

$y = \frac{18}{- 3} + \frac{- 3 x}{- 3}$

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

$y = \frac{18}{- 3} + \frac{- 3 x}{- 3}$

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

Simplify the right side.

Simplify each term.

Divide $18$ by $- 3$ .

$y = - 6 + \frac{- 3 x}{- 3}$

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

Cancel the common factor of $- 3$ .

Cancel the common factor.

$y = - 6 + \frac{- 3 x}{- 3}$

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

Divide $x$ by $1$ .

$y = - 6 + x$

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

$y = - 6 + x$

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

$y = - 6 + x$

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

$y = - 6 + x$

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

$y = - 6 + x$

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

Step 5

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

$(2, - 4)$

Step 6

Solve by Graphing 5x+2y=2 , 3x-3y=18

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