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

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

Step 1

Rewrite the equation as $y + 3 = 3 x$ .

$y + 3 = 3 x$

$6 x - 3 = 2 y$

Step 2

Subtract $3$ from both sides of the equation.

$y = 3 x - 3$

$6 x - 3 = 2 y$

Step 3

Rewrite the equation as $2 y = 6 x - 3$ .

$2 y = 6 x - 3$

$y = 3 x - 3$

Step 4

Divide each term in $2 y = 6 x - 3$ by $2$ and simplify.

Divide each term in $2 y = 6 x - 3$ by $2$ .

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

$y = 3 x - 3$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

$y = 3 x - 3$

Divide $y$ by $1$ .

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

$y = 3 x - 3$

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

$y = 3 x - 3$

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

$y = 3 x - 3$

Simplify the right side.

Simplify each term.

Cancel the common factor of $6$ and $2$ .

Factor $2$ out of $6 x$ .

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

$y = 3 x - 3$

Cancel the common factors.

Factor $2$ out of $2$ .

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

$y = 3 x - 3$

Cancel the common factor.

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

$y = 3 x - 3$

Rewrite the expression.

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

$y = 3 x - 3$

Divide $3 x$ by $1$ .

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

$y = 3 x - 3$

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

$y = 3 x - 3$

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

$y = 3 x - 3$

Move the negative in front of the fraction.

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

$y = 3 x - 3$

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

$y = 3 x - 3$

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

$y = 3 x - 3$

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

$y = 3 x - 3$

Step 5

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

No solution

Step 6

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

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