Solve by Graphing 5x-2y=3 , 15x-6y=9

$5 x - 2 y = 3$ , $15 x - 6 y = 9$

Step 1

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

$- 2 y = 3 - 5 x$

$15 x - 6 y = 9$

Step 2

Divide each term in $- 2 y = 3 - 5 x$ by $- 2$ and simplify.

Divide each term in $- 2 y = 3 - 5 x$ by $- 2$ .

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

$15 x - 6 y = 9$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

$15 x - 6 y = 9$

Divide $y$ by $1$ .

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

$15 x - 6 y = 9$

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

$15 x - 6 y = 9$

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

$15 x - 6 y = 9$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

$15 x - 6 y = 9$

Dividing two negative values results in a positive value.

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

$15 x - 6 y = 9$

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

$15 x - 6 y = 9$

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

$15 x - 6 y = 9$

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

$15 x - 6 y = 9$

Step 3

Subtract $15 x$ from both sides of the equation.

$- 6 y = 9 - 15 x$

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

Step 4

Divide each term in $- 6 y = 9 - 15 x$ by $- 6$ and simplify.

Divide each term in $- 6 y = 9 - 15 x$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{9}{- 6} + \frac{- 15 x}{- 6}$

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

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{9}{- 6} + \frac{- 15 x}{- 6}$

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

Divide $y$ by $1$ .

$y = \frac{9}{- 6} + \frac{- 15 x}{- 6}$

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

$y = \frac{9}{- 6} + \frac{- 15 x}{- 6}$

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

$y = \frac{9}{- 6} + \frac{- 15 x}{- 6}$

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $9$ and $- 6$ .

Factor $3$ out of $9$ .

$y = \frac{3 (3)}{- 6} + \frac{- 15 x}{- 6}$

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

Cancel the common factors.

Factor $3$ out of $- 6$ .

$y = \frac{3 \cdot 3}{3 \cdot - 2} + \frac{- 15 x}{- 6}$

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

Cancel the common factor.

$y = \frac{3 \cdot 3}{3 \cdot - 2} + \frac{- 15 x}{- 6}$

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

Rewrite the expression.

$y = \frac{3}{- 2} + \frac{- 15 x}{- 6}$

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

$y = \frac{3}{- 2} + \frac{- 15 x}{- 6}$

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

$y = \frac{3}{- 2} + \frac{- 15 x}{- 6}$

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

Move the negative in front of the fraction.

$y = - \frac{3}{2} + \frac{- 15 x}{- 6}$

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

Cancel the common factor of $- 15$ and $- 6$ .

Factor $- 3$ out of $- 15 x$ .

$y = - \frac{3}{2} + \frac{- 3 (5 x)}{- 6}$

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

Cancel the common factors.

Factor $- 3$ out of $- 6$ .

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

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

Cancel the common factor.

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

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

Rewrite the expression.

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

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

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

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

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

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

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

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

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

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

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

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

Step 5

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

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

Step 6

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