Solve the System of Equations 1/2x+7y=12 3/4x-3/2y=6

$\frac{1}{2} x + 7 y = 12$ $\frac{3}{4} x - \frac{3}{2} y = 6$

Solve for $y$ in $\frac{1}{2} x + 7 y = 12$ .

Combine $\frac{1}{2}$ and $x$ .

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

$\frac{3}{4} x - \frac{3}{2} y = 6$

Subtract $\frac{x}{2}$ from both sides of the equation.

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

$\frac{3}{4} x - \frac{3}{2} y = 6$

Divide each term in $7 y = 12 - \frac{x}{2}$ by $7$ and simplify.

Divide each term in $7 y = 12 - \frac{x}{2}$ by $7$ .

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

$\frac{3}{4} x - \frac{3}{2} y = 6$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

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

$\frac{3}{4} x - \frac{3}{2} y = 6$

Divide $y$ by $1$ .

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

$\frac{3}{4} x - \frac{3}{2} y = 6$

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

$\frac{3}{4} x - \frac{3}{2} y = 6$

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

$\frac{3}{4} x - \frac{3}{2} y = 6$

Simplify the right side.

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{12}{7} - \frac{x}{2} \cdot \frac{1}{7}$

$\frac{3}{4} x - \frac{3}{2} y = 6$

Multiply $- \frac{x}{2} \cdot \frac{1}{7}$ .

Multiply $\frac{1}{7}$ by $\frac{x}{2}$ .

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

$\frac{3}{4} x - \frac{3}{2} y = 6$

Multiply $7$ by $2$ .

$y = \frac{12}{7} - \frac{x}{14}$

$\frac{3}{4} x - \frac{3}{2} y = 6$

$y = \frac{12}{7} - \frac{x}{14}$

$\frac{3}{4} x - \frac{3}{2} y = 6$

$y = \frac{12}{7} - \frac{x}{14}$

$\frac{3}{4} x - \frac{3}{2} y = 6$

$y = \frac{12}{7} - \frac{x}{14}$

$\frac{3}{4} x - \frac{3}{2} y = 6$

$y = \frac{12}{7} - \frac{x}{14}$

$\frac{3}{4} x - \frac{3}{2} y = 6$

$y = \frac{12}{7} - \frac{x}{14}$

$\frac{3}{4} x - \frac{3}{2} y = 6$

Replace all occurrences of $y$ with $\frac{12}{7} - \frac{x}{14}$ in each equation.

Replace all occurrences of $y$ in $\frac{3}{4} x - \frac{3}{2} y = 6$ with $\frac{12}{7} - \frac{x}{14}$ .

$\frac{3}{4} x - \frac{3}{2} \cdot (\frac{12}{7} - \frac{x}{14}) = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Simplify the left side.

Simplify $\frac{3}{4} x - \frac{3}{2} \cdot (\frac{12}{7} - \frac{x}{14})$ .

Simplify each term.

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

$\frac{3 x}{4} - \frac{3}{2} \cdot (\frac{12}{7} - \frac{x}{14}) = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Apply the distributive property.

$\frac{3 x}{4} - \frac{3}{2} \cdot \frac{12}{7} - \frac{3}{2} \cdot (- \frac{x}{14}) = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Cancel the common factor of $2$ .

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

$\frac{3 x}{4} + \frac{- 3}{2} \cdot \frac{12}{7} - \frac{3}{2} \cdot (- \frac{x}{14}) = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Factor $2$ out of $12$ .

$\frac{3 x}{4} + \frac{- 3}{2} \cdot \frac{2 (6)}{7} - \frac{3}{2} \cdot (- \frac{x}{14}) = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Cancel the common factor.

$\frac{3 x}{4} + \frac{- 3}{2} \cdot \frac{2 \cdot 6}{7} - \frac{3}{2} \cdot (- \frac{x}{14}) = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Rewrite the expression.

$\frac{3 x}{4} - 3 (\frac{6}{7}) - \frac{3}{2} \cdot (- \frac{x}{14}) = 6$

$y = \frac{12}{7} - \frac{x}{14}$

$\frac{3 x}{4} - 3 (\frac{6}{7}) - \frac{3}{2} \cdot (- \frac{x}{14}) = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Combine $- 3$ and $\frac{6}{7}$ .

$\frac{3 x}{4} + \frac{- 3 \cdot 6}{7} - \frac{3}{2} \cdot (- \frac{x}{14}) = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Multiply $- 3$ by $6$ .

$\frac{3 x}{4} + \frac{- 18}{7} - \frac{3}{2} \cdot (- \frac{x}{14}) = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Multiply $- \frac{3}{2} (- \frac{x}{14})$ .

Multiply $- 1$ by $- 1$ .

$\frac{3 x}{4} + \frac{- 18}{7} + 1 (\frac{3}{2}) \cdot \frac{x}{14} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Multiply $\frac{3}{2}$ by $1$ .

$\frac{3 x}{4} + \frac{- 18}{7} + \frac{3}{2} \cdot \frac{x}{14} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Multiply $\frac{3}{2}$ by $\frac{x}{14}$ .

$\frac{3 x}{4} + \frac{- 18}{7} + \frac{3 x}{2 \cdot 14} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Multiply $2$ by $14$ .

$\frac{3 x}{4} + \frac{- 18}{7} + \frac{3 x}{28} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

$\frac{3 x}{4} + \frac{- 18}{7} + \frac{3 x}{28} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Move the negative in front of the fraction.

$\frac{3 x}{4} - \frac{18}{7} + \frac{3 x}{28} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

$\frac{3 x}{4} - \frac{18}{7} + \frac{3 x}{28} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

To write $\frac{3 x}{4}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{3 x}{4} \cdot \frac{7}{7} + \frac{3 x}{28} - \frac{18}{7} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Write each expression with a common denominator of $28$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{3 x \cdot 7}{4 \cdot 7} + \frac{3 x}{28} - \frac{18}{7} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Multiply $4$ by $7$ .

$\frac{3 x \cdot 7}{28} + \frac{3 x}{28} - \frac{18}{7} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

$\frac{3 x \cdot 7}{28} + \frac{3 x}{28} - \frac{18}{7} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Combine the numerators over the common denominator.

$\frac{3 x \cdot 7 + 3 x}{28} - \frac{18}{7} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Simplify each term.

Simplify the numerator.

Factor $3 x$ out of $3 x \cdot 7 + 3 x$ .

Factor $3 x$ out of $3 x \cdot 7$ .

$\frac{3 x (7) + 3 x}{28} - \frac{18}{7} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Factor $3 x$ out of $3 x$ .

$\frac{3 x (7) + 3 x (1)}{28} - \frac{18}{7} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Factor $3 x$ out of $3 x (7) + 3 x (1)$ .

$\frac{3 x (7 + 1)}{28} - \frac{18}{7} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

$\frac{3 x (7 + 1)}{28} - \frac{18}{7} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Add $7$ and $1$ .

$\frac{3 x \cdot 8}{28} - \frac{18}{7} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Multiply $8$ by $3$ .

$\frac{24 x}{28} - \frac{18}{7} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

$\frac{24 x}{28} - \frac{18}{7} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Cancel the common factor of $24$ and $28$ .

Factor $4$ out of $24 x$ .

$\frac{4 (6 x)}{28} - \frac{18}{7} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Cancel the common factors.

Factor $4$ out of $28$ .

$\frac{4 (6 x)}{4 (7)} - \frac{18}{7} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Cancel the common factor.

$\frac{4 (6 x)}{4 \cdot 7} - \frac{18}{7} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Rewrite the expression.

$\frac{6 x}{7} - \frac{18}{7} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

$\frac{6 x}{7} - \frac{18}{7} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

$\frac{6 x}{7} - \frac{18}{7} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

$\frac{6 x}{7} - \frac{18}{7} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

$\frac{6 x}{7} - \frac{18}{7} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

$\frac{6 x}{7} - \frac{18}{7} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

$\frac{6 x}{7} - \frac{18}{7} = 6$

$y = \frac{12}{7} - \frac{x}{14}$

Solve for $x$ in $\frac{6 x}{7} - \frac{18}{7} = 6$ .

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

Add $\frac{18}{7}$ to both sides of the equation.

$\frac{6 x}{7} = 6 + \frac{18}{7}$

$y = \frac{12}{7} - \frac{x}{14}$

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

$\frac{6 x}{7} = 6 \cdot \frac{7}{7} + \frac{18}{7}$

$y = \frac{12}{7} - \frac{x}{14}$

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

$\frac{6 x}{7} = \frac{6 \cdot 7}{7} + \frac{18}{7}$

$y = \frac{12}{7} - \frac{x}{14}$

Combine the numerators over the common denominator.

$\frac{6 x}{7} = \frac{6 \cdot 7 + 18}{7}$

$y = \frac{12}{7} - \frac{x}{14}$

Simplify the numerator.

Multiply $6$ by $7$ .

$\frac{6 x}{7} = \frac{42 + 18}{7}$

$y = \frac{12}{7} - \frac{x}{14}$

Add $42$ and $18$ .

$\frac{6 x}{7} = \frac{60}{7}$

$y = \frac{12}{7} - \frac{x}{14}$

$\frac{6 x}{7} = \frac{60}{7}$

$y = \frac{12}{7} - \frac{x}{14}$

$\frac{6 x}{7} = \frac{60}{7}$

$y = \frac{12}{7} - \frac{x}{14}$

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

$6 x = 60$

$y = \frac{12}{7} - \frac{x}{14}$

Divide each term in $6 x = 60$ by $6$ and simplify.

Divide each term in $6 x = 60$ by $6$ .

$\frac{6 x}{6} = \frac{60}{6}$

$y = \frac{12}{7} - \frac{x}{14}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{60}{6}$

$y = \frac{12}{7} - \frac{x}{14}$

Divide $x$ by $1$ .

$x = \frac{60}{6}$

$y = \frac{12}{7} - \frac{x}{14}$

$x = \frac{60}{6}$

$y = \frac{12}{7} - \frac{x}{14}$

$x = \frac{60}{6}$

$y = \frac{12}{7} - \frac{x}{14}$

Simplify the right side.

Divide $60$ by $6$ .

$x = 10$

$y = \frac{12}{7} - \frac{x}{14}$

$x = 10$

$y = \frac{12}{7} - \frac{x}{14}$

$x = 10$

$y = \frac{12}{7} - \frac{x}{14}$

$x = 10$

$y = \frac{12}{7} - \frac{x}{14}$

Replace all occurrences of $x$ with $10$ in each equation.

Replace all occurrences of $x$ in $y = \frac{12}{7} - \frac{x}{14}$ with $10$ .

$y = \frac{12}{7} - \frac{10}{14}$

$x = 10$

Simplify the right side.

Simplify $\frac{12}{7} - \frac{10}{14}$ .

Cancel the common factor of $10$ and $14$ .

Factor $2$ out of $10$ .

$y = \frac{12}{7} - \frac{2 (5)}{14}$

$x = 10$

Cancel the common factors.

Factor $2$ out of $14$ .

$y = \frac{12}{7} - \frac{2 \cdot 5}{2 \cdot 7}$

$x = 10$

Cancel the common factor.

$y = \frac{12}{7} - \frac{2 \cdot 5}{2 \cdot 7}$

$x = 10$

Rewrite the expression.

$y = \frac{12}{7} - \frac{5}{7}$

$x = 10$

$y = \frac{12}{7} - \frac{5}{7}$

$x = 10$

$y = \frac{12}{7} - \frac{5}{7}$

$x = 10$

Combine the numerators over the common denominator.

$y = \frac{12 - 5}{7}$

$x = 10$

Simplify the expression.

Subtract $5$ from $12$ .

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

$x = 10$

Divide $7$ by $7$ .

$y = 1$

$x = 10$

$y = 1$

$x = 10$

$y = 1$

$x = 10$

$y = 1$

$x = 10$

$y = 1$

$x = 10$

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

$(10, 1)$

The result can be shown in multiple forms.

Point Form:

$(10, 1)$

Equation Form:

$x = 10, y = 1$

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