Solve the System of Equations 2x+4y=8 3x=12+4y

$2 x + 4 y = 8$ $3 x = 12 + 4 y$

Step 1

Divide each term in $3 x = 12 + 4 y$ by $3$ and simplify.

Divide each term in $3 x = 12 + 4 y$ by $3$ .

$\frac{3 x}{3} = \frac{12}{3} + \frac{4 y}{3}$

$2 x + 4 y = 8$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{12}{3} + \frac{4 y}{3}$

$2 x + 4 y = 8$

Divide $x$ by $1$ .

$x = \frac{12}{3} + \frac{4 y}{3}$

$2 x + 4 y = 8$

$x = \frac{12}{3} + \frac{4 y}{3}$

$2 x + 4 y = 8$

$x = \frac{12}{3} + \frac{4 y}{3}$

$2 x + 4 y = 8$

Simplify the right side.

Divide $12$ by $3$ .

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

$2 x + 4 y = 8$

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

$2 x + 4 y = 8$

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

$2 x + 4 y = 8$

Step 2

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

Replace all occurrences of $x$ in $2 x + 4 y = 8$ with $4 + \frac{4 y}{3}$ .

$2 (4 + \frac{4 y}{3}) + 4 y = 8$

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

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

$2 \cdot 4 + 2 (\frac{4 y}{3}) + 4 y = 8$

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

Multiply $2$ by $4$ .

$8 + 2 (\frac{4 y}{3}) + 4 y = 8$

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

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

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

$8 + \frac{2 (4 y)}{3} + 4 y = 8$

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

Multiply $4$ by $2$ .

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

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

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

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

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

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

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

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

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

Simplify terms.

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

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

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

Combine the numerators over the common denominator.

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

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

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

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

Simplify the numerator.

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

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

$8 + \frac{4 y (2) + 4 y \cdot 3}{3} = 8$

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

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

$8 + \frac{4 y (2) + 4 y (3)}{3} = 8$

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

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

$8 + \frac{4 y (2 + 3)}{3} = 8$

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

$8 + \frac{4 y (2 + 3)}{3} = 8$

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

Add $2$ and $3$ .

$8 + \frac{4 y \cdot 5}{3} = 8$

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

Multiply $5$ by $4$ .

$8 + \frac{20 y}{3} = 8$

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

$8 + \frac{20 y}{3} = 8$

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

$8 + \frac{20 y}{3} = 8$

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

$8 + \frac{20 y}{3} = 8$

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

$8 + \frac{20 y}{3} = 8$

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

Step 3

Solve for $y$ in $8 + \frac{20 y}{3} = 8$ .

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

Subtract $8$ from both sides of the equation.

$\frac{20 y}{3} = 8 - 8$

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

Subtract $8$ from $8$ .

$\frac{20 y}{3} = 0$

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

$\frac{20 y}{3} = 0$

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

Set the numerator equal to zero.

$20 y = 0$

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

Divide each term in $20 y = 0$ by $20$ and simplify.

Divide each term in $20 y = 0$ by $20$ .

$\frac{20 y}{20} = \frac{0}{20}$

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

Simplify the left side.

Cancel the common factor of $20$ .

Cancel the common factor.

$\frac{20 y}{20} = \frac{0}{20}$

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

Divide $y$ by $1$ .

$y = \frac{0}{20}$

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

$y = \frac{0}{20}$

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

$y = \frac{0}{20}$

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

Simplify the right side.

Divide $0$ by $20$ .

$y = 0$

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

$y = 0$

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

$y = 0$

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

$y = 0$

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

Step 4

Replace all occurrences of $y$ with $0$ in each equation.

Replace all occurrences of $y$ in $x = 4 + \frac{4 y}{3}$ with $0$ .

$x = 4 + \frac{4 (0)}{3}$

$y = 0$

Simplify the right side.

Simplify $4 + \frac{4 (0)}{3}$ .

Multiply $4$ by $0$ .

$x = 4 + \frac{0}{3}$

$y = 0$

Divide $0$ by $3$ .

$x = 4 + 0$

$y = 0$

Add $4$ and $0$ .

$x = 4$

$y = 0$

$x = 4$

$y = 0$

$x = 4$

$y = 0$

$x = 4$

$y = 0$

Step 5

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

$(4, 0)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, 0)$

Equation Form:

$x = 4, y = 0$

Step 7

Solve the System of Equations 2x+4y=8 3x=12+4y

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