Solve the System of Equations y=4/7x 2/3x=y+5/7

$y = \frac{4}{7} x$ $\frac{2}{3} x = y + \frac{5}{7}$

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

$y = \frac{4 x}{7}$

$\frac{2}{3} x = y + \frac{5}{7}$

Replace all occurrences of $y$ with $\frac{4 x}{7}$ in each equation.

Replace all occurrences of $y$ in $\frac{2}{3} x = y + \frac{5}{7}$ with $\frac{4 x}{7}$ .

$\frac{2}{3} x = (\frac{4 x}{7}) + \frac{5}{7}$

$y = \frac{4 x}{7}$

Simplify $\frac{2}{3} x = (\frac{4 x}{7}) + \frac{5}{7}$ .

Simplify the left side.

Combine $\frac{2}{3}$ and $x$ .

$\frac{2 x}{3} = (\frac{4 x}{7}) + \frac{5}{7}$

$y = \frac{4 x}{7}$

$\frac{2 x}{3} = (\frac{4 x}{7}) + \frac{5}{7}$

$y = \frac{4 x}{7}$

Simplify the right side.

Remove parentheses.

$\frac{2 x}{3} = \frac{4 x}{7} + \frac{5}{7}$

$y = \frac{4 x}{7}$

$\frac{2 x}{3} = \frac{4 x}{7} + \frac{5}{7}$

$y = \frac{4 x}{7}$

$\frac{2 x}{3} = \frac{4 x}{7} + \frac{5}{7}$

$y = \frac{4 x}{7}$

$\frac{2 x}{3} = \frac{4 x}{7} + \frac{5}{7}$

$y = \frac{4 x}{7}$

Solve for $x$ in $\frac{2 x}{3} = \frac{4 x}{7} + \frac{5}{7}$ .

Multiply both sides by $3$ .

$\frac{2 x}{3} \cdot 3 = (\frac{4 x}{7} + \frac{5}{7}) \cdot 3$

$y = \frac{4 x}{7}$

Simplify.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{2 x}{3} \cdot 3 = (\frac{4 x}{7} + \frac{5}{7}) \cdot 3$

$y = \frac{4 x}{7}$

Rewrite the expression.

$2 x = (\frac{4 x}{7} + \frac{5}{7}) \cdot 3$

$y = \frac{4 x}{7}$

$2 x = (\frac{4 x}{7} + \frac{5}{7}) \cdot 3$

$y = \frac{4 x}{7}$

$2 x = (\frac{4 x}{7} + \frac{5}{7}) \cdot 3$

$y = \frac{4 x}{7}$

Simplify the right side.

Simplify $(\frac{4 x}{7} + \frac{5}{7}) \cdot 3$ .

Apply the distributive property.

$2 x = \frac{4 x}{7} \cdot 3 + \frac{5}{7} \cdot 3$

$y = \frac{4 x}{7}$

Multiply $\frac{4 x}{7} \cdot 3$ .

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

$2 x = \frac{4 x \cdot 3}{7} + \frac{5}{7} \cdot 3$

$y = \frac{4 x}{7}$

Multiply $3$ by $4$ .

$2 x = \frac{12 x}{7} + \frac{5}{7} \cdot 3$

$y = \frac{4 x}{7}$

$2 x = \frac{12 x}{7} + \frac{5}{7} \cdot 3$

$y = \frac{4 x}{7}$

Multiply $\frac{5}{7} \cdot 3$ .

Combine $\frac{5}{7}$ and $3$ .

$2 x = \frac{12 x}{7} + \frac{5 \cdot 3}{7}$

$y = \frac{4 x}{7}$

Multiply $5$ by $3$ .

$2 x = \frac{12 x}{7} + \frac{15}{7}$

$y = \frac{4 x}{7}$

$2 x = \frac{12 x}{7} + \frac{15}{7}$

$y = \frac{4 x}{7}$

$2 x = \frac{12 x}{7} + \frac{15}{7}$

$y = \frac{4 x}{7}$

$2 x = \frac{12 x}{7} + \frac{15}{7}$

$y = \frac{4 x}{7}$

$2 x = \frac{12 x}{7} + \frac{15}{7}$

$y = \frac{4 x}{7}$

Solve for $x$ .

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

Subtract $\frac{12 x}{7}$ from both sides of the equation.

$2 x - \frac{12 x}{7} = \frac{15}{7}$

$y = \frac{4 x}{7}$

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

$2 x \cdot \frac{7}{7} - \frac{12 x}{7} = \frac{15}{7}$

$y = \frac{4 x}{7}$

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

$\frac{2 x \cdot 7}{7} - \frac{12 x}{7} = \frac{15}{7}$

$y = \frac{4 x}{7}$

Combine the numerators over the common denominator.

$\frac{2 x \cdot 7 - 12 x}{7} = \frac{15}{7}$

$y = \frac{4 x}{7}$

Simplify the numerator.

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

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

$\frac{2 x (7) - 12 x}{7} = \frac{15}{7}$

$y = \frac{4 x}{7}$

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

$\frac{2 x (7) + 2 x (- 6)}{7} = \frac{15}{7}$

$y = \frac{4 x}{7}$

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

$\frac{2 x (7 - 6)}{7} = \frac{15}{7}$

$y = \frac{4 x}{7}$

$\frac{2 x (7 - 6)}{7} = \frac{15}{7}$

$y = \frac{4 x}{7}$

Subtract $6$ from $7$ .

$\frac{2 x \cdot 1}{7} = \frac{15}{7}$

$y = \frac{4 x}{7}$

Multiply $2$ by $1$ .

$\frac{2 x}{7} = \frac{15}{7}$

$y = \frac{4 x}{7}$

$\frac{2 x}{7} = \frac{15}{7}$

$y = \frac{4 x}{7}$

$\frac{2 x}{7} = \frac{15}{7}$

$y = \frac{4 x}{7}$

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

$2 x = 15$

$y = \frac{4 x}{7}$

Divide each term in $2 x = 15$ by $2$ and simplify.

Divide each term in $2 x = 15$ by $2$ .

$\frac{2 x}{2} = \frac{15}{2}$

$y = \frac{4 x}{7}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{15}{2}$

$y = \frac{4 x}{7}$

Divide $x$ by $1$ .

$x = \frac{15}{2}$

$y = \frac{4 x}{7}$

$x = \frac{15}{2}$

$y = \frac{4 x}{7}$

$x = \frac{15}{2}$

$y = \frac{4 x}{7}$

$x = \frac{15}{2}$

$y = \frac{4 x}{7}$

$x = \frac{15}{2}$

$y = \frac{4 x}{7}$

$x = \frac{15}{2}$

$y = \frac{4 x}{7}$

Replace all occurrences of $x$ with $\frac{15}{2}$ in each equation.

Replace all occurrences of $x$ in $y = \frac{4 x}{7}$ with $\frac{15}{2}$ .

$y = \frac{4 (\frac{15}{2})}{7}$

$x = \frac{15}{2}$

Simplify the right side.

Simplify $\frac{4 (\frac{15}{2})}{7}$ .

Combine $4$ and $\frac{15}{2}$ .

$y = \frac{\frac{4 \cdot 15}{2}}{7}$

$x = \frac{15}{2}$

Simplify the expression.

Multiply $4$ by $15$ .

$y = \frac{\frac{60}{2}}{7}$

$x = \frac{15}{2}$

Divide $60$ by $2$ .

$y = \frac{30}{7}$

$x = \frac{15}{2}$

$y = \frac{30}{7}$

$x = \frac{15}{2}$

$y = \frac{30}{7}$

$x = \frac{15}{2}$

$y = \frac{30}{7}$

$x = \frac{15}{2}$

$y = \frac{30}{7}$

$x = \frac{15}{2}$

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

$(\frac{15}{2}, \frac{30}{7})$

The result can be shown in multiple forms.

Point Form:

$(\frac{15}{2}, \frac{30}{7})$

Equation Form:

$x = \frac{15}{2}, y = \frac{30}{7}$

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