Solve the System of Equations 2x-6=4y 7y=-3x+9

$2 x - 6 = 4 y$ $7 y = - 3 x + 9$

Step 1

Divide each term in $7 y = - 3 x + 9$ by $7$ and simplify.

Divide each term in $7 y = - 3 x + 9$ by $7$ .

$\frac{7 y}{7} = \frac{- 3 x}{7} + \frac{9}{7}$

$2 x - 6 = 4 y$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{- 3 x}{7} + \frac{9}{7}$

$2 x - 6 = 4 y$

Divide $y$ by $1$ .

$y = \frac{- 3 x}{7} + \frac{9}{7}$

$2 x - 6 = 4 y$

$y = \frac{- 3 x}{7} + \frac{9}{7}$

$2 x - 6 = 4 y$

$y = \frac{- 3 x}{7} + \frac{9}{7}$

$2 x - 6 = 4 y$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{3 x}{7} + \frac{9}{7}$

$2 x - 6 = 4 y$

$y = - \frac{3 x}{7} + \frac{9}{7}$

$2 x - 6 = 4 y$

$y = - \frac{3 x}{7} + \frac{9}{7}$

$2 x - 6 = 4 y$

Step 2

Replace all occurrences of $y$ with $- \frac{3 x}{7} + \frac{9}{7}$ in each equation.

Replace all occurrences of $y$ in $2 x - 6 = 4 y$ with $- \frac{3 x}{7} + \frac{9}{7}$ .

$2 x - 6 = 4 (- \frac{3 x}{7} + \frac{9}{7})$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Simplify the right side.

Simplify $4 (- \frac{3 x}{7} + \frac{9}{7})$ .

Apply the distributive property.

$2 x - 6 = 4 (- \frac{3 x}{7}) + 4 (\frac{9}{7})$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Multiply $4 (- \frac{3 x}{7})$ .

Multiply $- 1$ by $4$ .

$2 x - 6 = - 4 \frac{3 x}{7} + 4 (\frac{9}{7})$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Combine $- 4$ and $\frac{3 x}{7}$ .

$2 x - 6 = \frac{- 4 (3 x)}{7} + 4 (\frac{9}{7})$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Multiply $3$ by $- 4$ .

$2 x - 6 = \frac{- 12 x}{7} + 4 (\frac{9}{7})$

$y = - \frac{3 x}{7} + \frac{9}{7}$

$2 x - 6 = \frac{- 12 x}{7} + 4 (\frac{9}{7})$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Multiply $4 (\frac{9}{7})$ .

Combine $4$ and $\frac{9}{7}$ .

$2 x - 6 = \frac{- 12 x}{7} + \frac{4 \cdot 9}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Multiply $4$ by $9$ .

$2 x - 6 = \frac{- 12 x}{7} + \frac{36}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

$2 x - 6 = \frac{- 12 x}{7} + \frac{36}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Move the negative in front of the fraction.

$2 x - 6 = - \frac{12 x}{7} + \frac{36}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

$2 x - 6 = - \frac{12 x}{7} + \frac{36}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

$2 x - 6 = - \frac{12 x}{7} + \frac{36}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

$2 x - 6 = - \frac{12 x}{7} + \frac{36}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Step 3

Solve for $x$ in $2 x - 6 = - \frac{12 x}{7} + \frac{36}{7}$ .

Move all terms containing $x$ to the left side of the equation.

Add $\frac{12 x}{7}$ to both sides of the equation.

$2 x - 6 + \frac{12 x}{7} = \frac{36}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

To write $2 x$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$2 x \cdot \frac{7}{7} + \frac{12 x}{7} - 6 = \frac{36}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Combine $2 x$ and $\frac{7}{7}$ .

$\frac{2 x \cdot 7}{7} + \frac{12 x}{7} - 6 = \frac{36}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Combine the numerators over the common denominator.

$\frac{2 x \cdot 7 + 12 x}{7} - 6 = \frac{36}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Simplify the numerator.

Factor $2 x$ out of $2 x \cdot 7 + 12 x$ .

Factor $2 x$ out of $2 x \cdot 7$ .

$\frac{2 x (7) + 12 x}{7} - 6 = \frac{36}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Factor $2 x$ out of $12 x$ .

$\frac{2 x (7) + 2 x (6)}{7} - 6 = \frac{36}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Factor $2 x$ out of $2 x (7) + 2 x (6)$ .

$\frac{2 x (7 + 6)}{7} - 6 = \frac{36}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

$\frac{2 x (7 + 6)}{7} - 6 = \frac{36}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Add $7$ and $6$ .

$\frac{2 x \cdot 13}{7} - 6 = \frac{36}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Multiply $13$ by $2$ .

$\frac{26 x}{7} - 6 = \frac{36}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

$\frac{26 x}{7} - 6 = \frac{36}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

$\frac{26 x}{7} - 6 = \frac{36}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Move all terms not containing $x$ to the right side of the equation.

Add $6$ to both sides of the equation.

$\frac{26 x}{7} = \frac{36}{7} + 6$

$y = - \frac{3 x}{7} + \frac{9}{7}$

To write $6$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{26 x}{7} = \frac{36}{7} + 6 \cdot \frac{7}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Combine $6$ and $\frac{7}{7}$ .

$\frac{26 x}{7} = \frac{36}{7} + \frac{6 \cdot 7}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Combine the numerators over the common denominator.

$\frac{26 x}{7} = \frac{36 + 6 \cdot 7}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Simplify the numerator.

Multiply $6$ by $7$ .

$\frac{26 x}{7} = \frac{36 + 42}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Add $36$ and $42$ .

$\frac{26 x}{7} = \frac{78}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

$\frac{26 x}{7} = \frac{78}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

$\frac{26 x}{7} = \frac{78}{7}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$26 x = 78$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Divide each term in $26 x = 78$ by $26$ and simplify.

Divide each term in $26 x = 78$ by $26$ .

$\frac{26 x}{26} = \frac{78}{26}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Simplify the left side.

Cancel the common factor of $26$ .

Cancel the common factor.

$\frac{26 x}{26} = \frac{78}{26}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Divide $x$ by $1$ .

$x = \frac{78}{26}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

$x = \frac{78}{26}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

$x = \frac{78}{26}$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Simplify the right side.

Divide $78$ by $26$ .

$x = 3$

$y = - \frac{3 x}{7} + \frac{9}{7}$

$x = 3$

$y = - \frac{3 x}{7} + \frac{9}{7}$

$x = 3$

$y = - \frac{3 x}{7} + \frac{9}{7}$

$x = 3$

$y = - \frac{3 x}{7} + \frac{9}{7}$

Step 4

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

Replace all occurrences of $x$ in $y = - \frac{3 x}{7} + \frac{9}{7}$ with $3$ .

$y = - \frac{3 (3)}{7} + \frac{9}{7}$

$x = 3$

Simplify the right side.

Simplify $- \frac{3 (3)}{7} + \frac{9}{7}$ .

Combine the numerators over the common denominator.

$y = \frac{- 3 \cdot 3 + 9}{7}$

$x = 3$

Simplify the expression.

Multiply $- 3$ by $3$ .

$y = \frac{- 9 + 9}{7}$

$x = 3$

Add $- 9$ and $9$ .

$y = \frac{0}{7}$

$x = 3$

Divide $0$ by $7$ .

$y = 0$

$x = 3$

$y = 0$

$x = 3$

$y = 0$

$x = 3$

$y = 0$

$x = 3$

$y = 0$

$x = 3$

Step 5

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

$(3, 0)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(3, 0)$

Equation Form:

$x = 3, y = 0$

Step 7

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