Solve the System of Equations Solve the system of equations 3x+2y=9 and 3x-y=0

Solve the system of equations $3 x + 2 y = 9$ and $3 x - y = 0$

Step 1

Solve for $x$ in $3 x + 2 y = 9$ .

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

$3 x = 9 - 2 y$

$3 x - y = 0$

Divide each term in $3 x = 9 - 2 y$ by $3$ and simplify.

Divide each term in $3 x = 9 - 2 y$ by $3$ .

$\frac{3 x}{3} = \frac{9}{3} + \frac{- 2 y}{3}$

$3 x - y = 0$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{9}{3} + \frac{- 2 y}{3}$

$3 x - y = 0$

Divide $x$ by $1$ .

$x = \frac{9}{3} + \frac{- 2 y}{3}$

$3 x - y = 0$

$x = \frac{9}{3} + \frac{- 2 y}{3}$

$3 x - y = 0$

$x = \frac{9}{3} + \frac{- 2 y}{3}$

$3 x - y = 0$

Simplify the right side.

Simplify each term.

Divide $9$ by $3$ .

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

$3 x - y = 0$

Move the negative in front of the fraction.

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

$3 x - y = 0$

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

$3 x - y = 0$

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

$3 x - y = 0$

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

$3 x - y = 0$

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

$3 x - y = 0$

Step 2

Replace all occurrences of $x$ with $3 - \frac{2 y}{3}$ in each equation.

Replace all occurrences of $x$ in $3 x - y = 0$ with $3 - \frac{2 y}{3}$ .

$3 (3 - \frac{2 y}{3}) - y = 0$

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

Simplify the left side.

Simplify $3 (3 - \frac{2 y}{3}) - y$ .

Simplify each term.

Apply the distributive property.

$3 \cdot 3 + 3 (- \frac{2 y}{3}) - y = 0$

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

Multiply $3$ by $3$ .

$9 + 3 (- \frac{2 y}{3}) - y = 0$

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

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2 y}{3}$ into the numerator.

$9 + 3 (\frac{- 2 y}{3}) - y = 0$

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

Cancel the common factor.

$9 + 3 (\frac{- 2 y}{3}) - y = 0$

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

Rewrite the expression.

$9 - 2 y - y = 0$

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

$9 - 2 y - y = 0$

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

$9 - 2 y - y = 0$

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

Subtract $y$ from $- 2 y$ .

$9 - 3 y = 0$

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

$9 - 3 y = 0$

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

$9 - 3 y = 0$

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

$9 - 3 y = 0$

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

Step 3

Solve for $y$ in $9 - 3 y = 0$ .

Subtract $9$ from both sides of the equation.

$- 3 y = - 9$

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

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

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

$\frac{- 3 y}{- 3} = \frac{- 9}{- 3}$

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 9}{- 3}$

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

Divide $y$ by $1$ .

$y = \frac{- 9}{- 3}$

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

$y = \frac{- 9}{- 3}$

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

$y = \frac{- 9}{- 3}$

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

Simplify the right side.

Divide $- 9$ by $- 3$ .

$y = 3$

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

$y = 3$

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

$y = 3$

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

$y = 3$

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

Step 4

Replace all occurrences of $y$ with $3$ in each equation.

Replace all occurrences of $y$ in $x = 3 - \frac{2 y}{3}$ with $3$ .

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

$y = 3$

Simplify the right side.

Simplify $3 - \frac{2 (3)}{3}$ .

Simplify each term.

Cancel the common factor of $3$ .

Cancel the common factor.

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

$y = 3$

Divide $2$ by $1$ .

$x = 3 - 1 \cdot 2$

$y = 3$

$x = 3 - 1 \cdot 2$

$y = 3$

Multiply $- 1$ by $2$ .

$x = 3 - 2$

$y = 3$

$x = 3 - 2$

$y = 3$

Subtract $2$ from $3$ .

$x = 1$

$y = 3$

$x = 1$

$y = 3$

$x = 1$

$y = 3$

$x = 1$

$y = 3$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(1, 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(1, 3)$

Equation Form:

$x = 1, y = 3$

Step 7

Solve the System of Equations Solve the system of equations 3x+2y=9 and 3x-y=0

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