Solve by Graphing 6x+3y=9 , y+2x=3

$6 x + 3 y = 9$ , $y + 2 x = 3$

Step 1

Subtract $6 x$ from both sides of the equation.

$3 y = 9 - 6 x$

$y + 2 x = 3$

Step 2

Divide each term in $3 y = 9 - 6 x$ by $3$ and simplify.

Divide each term in $3 y = 9 - 6 x$ by $3$ .

$\frac{3 y}{3} = \frac{9}{3} + \frac{- 6 x}{3}$

$y + 2 x = 3$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{9}{3} + \frac{- 6 x}{3}$

$y + 2 x = 3$

Divide $y$ by $1$ .

$y = \frac{9}{3} + \frac{- 6 x}{3}$

$y + 2 x = 3$

$y = \frac{9}{3} + \frac{- 6 x}{3}$

$y + 2 x = 3$

$y = \frac{9}{3} + \frac{- 6 x}{3}$

$y + 2 x = 3$

Simplify the right side.

Simplify each term.

Divide $9$ by $3$ .

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

$y + 2 x = 3$

Cancel the common factor of $- 6$ and $3$ .

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

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

$y + 2 x = 3$

Cancel the common factors.

Factor $3$ out of $3$ .

$y = 3 + \frac{3 (- 2 x)}{3 (1)}$

$y + 2 x = 3$

Cancel the common factor.

$y = 3 + \frac{3 (- 2 x)}{3 \cdot 1}$

$y + 2 x = 3$

Rewrite the expression.

$y = 3 + \frac{- 2 x}{1}$

$y + 2 x = 3$

Divide $- 2 x$ by $1$ .

$y = 3 - 2 x$

$y + 2 x = 3$

$y = 3 - 2 x$

$y + 2 x = 3$

$y = 3 - 2 x$

$y + 2 x = 3$

$y = 3 - 2 x$

$y + 2 x = 3$

$y = 3 - 2 x$

$y + 2 x = 3$

$y = 3 - 2 x$

$y + 2 x = 3$

Step 3

Subtract $2 x$ from both sides of the equation.

$y = 3 - 2 x$

Step 4

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

$y = - 2 x + 3$

Step 5

Solve by Graphing 6x+3y=9 , y+2x=3

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