Find the Intersection (and) 2x+3y=12 , 3x-y=9

$2 x + 3 y = 12$ , $3 x - y = 9$

Simplify the first inequality.

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

$2 x = 12 - 3 y$

Divide each term by $2$ and simplify.

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Divide each term in $2 x = 12 - 3 y$ by $2$ .

$\frac{2 x}{2} = \frac{12}{2} + \frac{- 3 y}{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2 x}{2} = \frac{12}{2} + \frac{- 3 y}{2}$

Divide $x$ by $1$ .

$x = \frac{12}{2} + \frac{- 3 y}{2}$

Simplify each term.

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Divide $12$ by $2$ .

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

Move the negative in front of the fraction.

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

Simplify the second inequality.

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Add $y$ to both sides of the equation.

$3 x = 9 + y$

Divide each term by $3$ and simplify.

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

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

Cancel the common factor of $3$ .

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Cancel the common factor.

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

Divide $x$ by $1$ .

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

Divide $9$ by $3$ .

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

Find the Intersection (and) 2x+3y=12 , 3x-y=9

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