Solve the System of Equations 3x-4y=-6 2x+4y=16

$3 x - 4 y = - 6$ $2 x + 4 y = 16$

Step 1

Solve for $x$ in $3 x - 4 y = - 6$ .

Add $4 y$ to both sides of the equation.

$3 x = - 6 + 4 y$

$2 x + 4 y = 16$

Divide each term in $3 x = - 6 + 4 y$ by $3$ and simplify.

Divide each term in $3 x = - 6 + 4 y$ by $3$ .

$\frac{3 x}{3} = \frac{- 6}{3} + \frac{4 y}{3}$

$2 x + 4 y = 16$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 6}{3} + \frac{4 y}{3}$

$2 x + 4 y = 16$

Divide $x$ by $1$ .

$x = \frac{- 6}{3} + \frac{4 y}{3}$

$2 x + 4 y = 16$

$x = \frac{- 6}{3} + \frac{4 y}{3}$

$2 x + 4 y = 16$

$x = \frac{- 6}{3} + \frac{4 y}{3}$

$2 x + 4 y = 16$

Simplify the right side.

Divide $- 6$ by $3$ .

$x = - 2 + \frac{4 y}{3}$

$2 x + 4 y = 16$

$x = - 2 + \frac{4 y}{3}$

$2 x + 4 y = 16$

$x = - 2 + \frac{4 y}{3}$

$2 x + 4 y = 16$

$x = - 2 + \frac{4 y}{3}$

$2 x + 4 y = 16$

Step 2

Replace all occurrences of $x$ with $- 2 + \frac{4 y}{3}$ in each equation.

Replace all occurrences of $x$ in $2 x + 4 y = 16$ with $- 2 + \frac{4 y}{3}$ .

$2 (- 2 + \frac{4 y}{3}) + 4 y = 16$

$x = - 2 + \frac{4 y}{3}$

Simplify the left side.

Simplify $2 (- 2 + \frac{4 y}{3}) + 4 y$ .

Simplify each term.

Apply the distributive property.

$2 \cdot - 2 + 2 (\frac{4 y}{3}) + 4 y = 16$

$x = - 2 + \frac{4 y}{3}$

Multiply $2$ by $- 2$ .

$- 4 + 2 (\frac{4 y}{3}) + 4 y = 16$

$x = - 2 + \frac{4 y}{3}$

Multiply $2 \frac{4 y}{3}$ .

Combine $2$ and $\frac{4 y}{3}$ .

$- 4 + \frac{2 (4 y)}{3} + 4 y = 16$

$x = - 2 + \frac{4 y}{3}$

Multiply $4$ by $2$ .

$- 4 + \frac{8 y}{3} + 4 y = 16$

$x = - 2 + \frac{4 y}{3}$

$- 4 + \frac{8 y}{3} + 4 y = 16$

$x = - 2 + \frac{4 y}{3}$

$- 4 + \frac{8 y}{3} + 4 y = 16$

$x = - 2 + \frac{4 y}{3}$

To write $4 y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- 4 + \frac{8 y}{3} + 4 y \cdot \frac{3}{3} = 16$

$x = - 2 + \frac{4 y}{3}$

Simplify terms.

Combine $4 y$ and $\frac{3}{3}$ .

$- 4 + \frac{8 y}{3} + \frac{4 y \cdot 3}{3} = 16$

$x = - 2 + \frac{4 y}{3}$

Combine the numerators over the common denominator.

$- 4 + \frac{8 y + 4 y \cdot 3}{3} = 16$

$x = - 2 + \frac{4 y}{3}$

$- 4 + \frac{8 y + 4 y \cdot 3}{3} = 16$

$x = - 2 + \frac{4 y}{3}$

Simplify the numerator.

Factor $4 y$ out of $8 y + 4 y \cdot 3$ .

Factor $4 y$ out of $8 y$ .

$- 4 + \frac{4 y (2) + 4 y \cdot 3}{3} = 16$

$x = - 2 + \frac{4 y}{3}$

Factor $4 y$ out of $4 y \cdot 3$ .

$- 4 + \frac{4 y (2) + 4 y (3)}{3} = 16$

$x = - 2 + \frac{4 y}{3}$

Factor $4 y$ out of $4 y (2) + 4 y (3)$ .

$- 4 + \frac{4 y (2 + 3)}{3} = 16$

$x = - 2 + \frac{4 y}{3}$

$- 4 + \frac{4 y (2 + 3)}{3} = 16$

$x = - 2 + \frac{4 y}{3}$

Add $2$ and $3$ .

$- 4 + \frac{4 y \cdot 5}{3} = 16$

$x = - 2 + \frac{4 y}{3}$

Multiply $5$ by $4$ .

$- 4 + \frac{20 y}{3} = 16$

$x = - 2 + \frac{4 y}{3}$

$- 4 + \frac{20 y}{3} = 16$

$x = - 2 + \frac{4 y}{3}$

$- 4 + \frac{20 y}{3} = 16$

$x = - 2 + \frac{4 y}{3}$

$- 4 + \frac{20 y}{3} = 16$

$x = - 2 + \frac{4 y}{3}$

$- 4 + \frac{20 y}{3} = 16$

$x = - 2 + \frac{4 y}{3}$

Step 3

Solve for $y$ in $- 4 + \frac{20 y}{3} = 16$ .

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

Add $4$ to both sides of the equation.

$\frac{20 y}{3} = 16 + 4$

$x = - 2 + \frac{4 y}{3}$

Add $16$ and $4$ .

$\frac{20 y}{3} = 20$

$x = - 2 + \frac{4 y}{3}$

$\frac{20 y}{3} = 20$

$x = - 2 + \frac{4 y}{3}$

Multiply both sides of the equation by $\frac{3}{20}$ .

$\frac{3}{20} \cdot \frac{20 y}{3} = \frac{3}{20} \cdot 20$

$x = - 2 + \frac{4 y}{3}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{20} \cdot \frac{20 y}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{20} \cdot \frac{20 y}{3} = \frac{3}{20} \cdot 20$

$x = - 2 + \frac{4 y}{3}$

Rewrite the expression.

$\frac{1}{20} \cdot (20 y) = \frac{3}{20} \cdot 20$

$x = - 2 + \frac{4 y}{3}$

$\frac{1}{20} \cdot (20 y) = \frac{3}{20} \cdot 20$

$x = - 2 + \frac{4 y}{3}$

Cancel the common factor of $20$ .

Factor $20$ out of $20 y$ .

$\frac{1}{20} \cdot (20 (y)) = \frac{3}{20} \cdot 20$

$x = - 2 + \frac{4 y}{3}$

Cancel the common factor.

$\frac{1}{20} \cdot (20 y) = \frac{3}{20} \cdot 20$

$x = - 2 + \frac{4 y}{3}$

Rewrite the expression.

$y = \frac{3}{20} \cdot 20$

$x = - 2 + \frac{4 y}{3}$

$y = \frac{3}{20} \cdot 20$

$x = - 2 + \frac{4 y}{3}$

$y = \frac{3}{20} \cdot 20$

$x = - 2 + \frac{4 y}{3}$

$y = \frac{3}{20} \cdot 20$

$x = - 2 + \frac{4 y}{3}$

Simplify the right side.

Cancel the common factor of $20$ .

Cancel the common factor.

$y = \frac{3}{20} \cdot 20$

$x = - 2 + \frac{4 y}{3}$

Rewrite the expression.

$y = 3$

$x = - 2 + \frac{4 y}{3}$

$y = 3$

$x = - 2 + \frac{4 y}{3}$

$y = 3$

$x = - 2 + \frac{4 y}{3}$

$y = 3$

$x = - 2 + \frac{4 y}{3}$

$y = 3$

$x = - 2 + \frac{4 y}{3}$

Step 4

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

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

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

$y = 3$

Simplify the right side.

Simplify $- 2 + \frac{4 (3)}{3}$ .

Multiply $4$ by $3$ .

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

$y = 3$

Divide $12$ by $3$ .

$x = - 2 + 4$

$y = 3$

Add $- 2$ and $4$ .

$x = 2$

$y = 3$

$x = 2$

$y = 3$

$x = 2$

$y = 3$

$x = 2$

$y = 3$

Step 5

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

$(2, 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(2, 3)$

Equation Form:

$x = 2, y = 3$

Step 7

Solve the System of Equations 3x-4y=-6 2x+4y=16

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