Solve the System of Equations 1/2x-1/4y=10 1/8x-1/8y=19

$\frac{1}{2} x - \frac{1}{4} y = 10$ $\frac{1}{8} x - \frac{1}{8} y = 19$

Solve for $x$ in $\frac{1}{2} x - \frac{1}{4} y = 10$ .

Simplify each term.

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

$\frac{x}{2} - \frac{1}{4} y = 10$

$\frac{1}{8} x - \frac{1}{8} y = 19$

Combine $y$ and $\frac{1}{4}$ .

$\frac{x}{2} - \frac{y}{4} = 10$

$\frac{1}{8} x - \frac{1}{8} y = 19$

$\frac{x}{2} - \frac{y}{4} = 10$

$\frac{1}{8} x - \frac{1}{8} y = 19$

Add $\frac{y}{4}$ to both sides of the equation.

$\frac{x}{2} = 10 + \frac{y}{4}$

$\frac{1}{8} x - \frac{1}{8} y = 19$

Multiply both sides of the equation by $2$ .

$2 (\frac{x}{2}) = 2 (10 + \frac{y}{4})$

$\frac{1}{8} x - \frac{1}{8} y = 19$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 (\frac{x}{2}) = 2 (10 + \frac{y}{4})$

$\frac{1}{8} x - \frac{1}{8} y = 19$

Rewrite the expression.

$x = 2 (10 + \frac{y}{4})$

$\frac{1}{8} x - \frac{1}{8} y = 19$

$x = 2 (10 + \frac{y}{4})$

$\frac{1}{8} x - \frac{1}{8} y = 19$

$x = 2 (10 + \frac{y}{4})$

$\frac{1}{8} x - \frac{1}{8} y = 19$

Simplify the right side.

Simplify $2 (10 + \frac{y}{4})$ .

Apply the distributive property.

$x = 2 \cdot 10 + 2 (\frac{y}{4})$

$\frac{1}{8} x - \frac{1}{8} y = 19$

Multiply $2$ by $10$ .

$x = 20 + 2 (\frac{y}{4})$

$\frac{1}{8} x - \frac{1}{8} y = 19$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$x = 20 + 2 (\frac{y}{2 (2)})$

$\frac{1}{8} x - \frac{1}{8} y = 19$

Cancel the common factor.

$x = 20 + 2 (\frac{y}{2 \cdot 2})$

$\frac{1}{8} x - \frac{1}{8} y = 19$

Rewrite the expression.

$x = 20 + \frac{y}{2}$

$\frac{1}{8} x - \frac{1}{8} y = 19$

$x = 20 + \frac{y}{2}$

$\frac{1}{8} x - \frac{1}{8} y = 19$

$x = 20 + \frac{y}{2}$

$\frac{1}{8} x - \frac{1}{8} y = 19$

$x = 20 + \frac{y}{2}$

$\frac{1}{8} x - \frac{1}{8} y = 19$

$x = 20 + \frac{y}{2}$

$\frac{1}{8} x - \frac{1}{8} y = 19$

Reorder $20$ and $\frac{y}{2}$ .

$x = \frac{y}{2} + 20$

$\frac{1}{8} x - \frac{1}{8} y = 19$

$x = \frac{y}{2} + 20$

$\frac{1}{8} x - \frac{1}{8} y = 19$

Replace all occurrences of $x$ with $\frac{y}{2} + 20$ in each equation.

Replace all occurrences of $x$ in $\frac{1}{8} x - \frac{1}{8} y = 19$ with $\frac{y}{2} + 20$ .

$\frac{1}{8} \cdot (\frac{y}{2} + 20) - \frac{1}{8} y = 19$

$x = \frac{y}{2} + 20$

Simplify the left side.

Simplify $\frac{1}{8} \cdot (\frac{y}{2} + 20) - \frac{1}{8} y$ .

Simplify each term.

Apply the distributive property.

$\frac{1}{8} \cdot \frac{y}{2} + \frac{1}{8} \cdot 20 - \frac{1}{8} y = 19$

$x = \frac{y}{2} + 20$

Multiply $\frac{1}{8} \cdot \frac{y}{2}$ .

Multiply $\frac{1}{8}$ by $\frac{y}{2}$ .

$\frac{y}{8 \cdot 2} + \frac{1}{8} \cdot 20 - \frac{1}{8} y = 19$

$x = \frac{y}{2} + 20$

Multiply $8$ by $2$ .

$\frac{y}{16} + \frac{1}{8} \cdot 20 - \frac{1}{8} y = 19$

$x = \frac{y}{2} + 20$

$\frac{y}{16} + \frac{1}{8} \cdot 20 - \frac{1}{8} y = 19$

$x = \frac{y}{2} + 20$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$\frac{y}{16} + \frac{1}{4 (2)} \cdot 20 - \frac{1}{8} y = 19$

$x = \frac{y}{2} + 20$

Factor $4$ out of $20$ .

$\frac{y}{16} + \frac{1}{4 \cdot 2} \cdot (4 \cdot 5) - \frac{1}{8} y = 19$

$x = \frac{y}{2} + 20$

Cancel the common factor.

$\frac{y}{16} + \frac{1}{4 \cdot 2} \cdot (4 \cdot 5) - \frac{1}{8} y = 19$

$x = \frac{y}{2} + 20$

Rewrite the expression.

$\frac{y}{16} + \frac{1}{2} \cdot 5 - \frac{1}{8} y = 19$

$x = \frac{y}{2} + 20$

$\frac{y}{16} + \frac{1}{2} \cdot 5 - \frac{1}{8} y = 19$

$x = \frac{y}{2} + 20$

Combine $\frac{1}{2}$ and $5$ .

$\frac{y}{16} + \frac{5}{2} - \frac{1}{8} y = 19$

$x = \frac{y}{2} + 20$

Combine $y$ and $\frac{1}{8}$ .

$\frac{y}{16} + \frac{5}{2} - \frac{y}{8} = 19$

$x = \frac{y}{2} + 20$

$\frac{y}{16} + \frac{5}{2} - \frac{y}{8} = 19$

$x = \frac{y}{2} + 20$

To write $- \frac{y}{8}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{y}{16} - \frac{y}{8} \cdot \frac{2}{2} + \frac{5}{2} = 19$

$x = \frac{y}{2} + 20$

Write each expression with a common denominator of $16$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{y}{8}$ by $\frac{2}{2}$ .

$\frac{y}{16} - \frac{y \cdot 2}{8 \cdot 2} + \frac{5}{2} = 19$

$x = \frac{y}{2} + 20$

Multiply $8$ by $2$ .

$\frac{y}{16} - \frac{y \cdot 2}{16} + \frac{5}{2} = 19$

$x = \frac{y}{2} + 20$

$\frac{y}{16} - \frac{y \cdot 2}{16} + \frac{5}{2} = 19$

$x = \frac{y}{2} + 20$

Combine the numerators over the common denominator.

$\frac{y - y \cdot 2}{16} + \frac{5}{2} = 19$

$x = \frac{y}{2} + 20$

Simplify each term.

Simplify the numerator.

Factor $y$ out of $y - y \cdot 2$ .

Raise $y$ to the power of $1$ .

$\frac{y - y \cdot 2}{16} + \frac{5}{2} = 19$

$x = \frac{y}{2} + 20$

Factor $y$ out of $y^{1}$ .

$\frac{y \cdot 1 - y \cdot 2}{16} + \frac{5}{2} = 19$

$x = \frac{y}{2} + 20$

Factor $y$ out of $- y \cdot 2$ .

$\frac{y \cdot 1 + y (- 1 \cdot 2)}{16} + \frac{5}{2} = 19$

$x = \frac{y}{2} + 20$

Factor $y$ out of $y \cdot 1 + y (- 1 \cdot 2)$ .

$\frac{y (1 - 1 \cdot 2)}{16} + \frac{5}{2} = 19$

$x = \frac{y}{2} + 20$

$\frac{y (1 - 1 \cdot 2)}{16} + \frac{5}{2} = 19$

$x = \frac{y}{2} + 20$

Multiply $- 1$ by $2$ .

$\frac{y (1 - 2)}{16} + \frac{5}{2} = 19$

$x = \frac{y}{2} + 20$

Subtract $2$ from $1$ .

$\frac{y \cdot - 1}{16} + \frac{5}{2} = 19$

$x = \frac{y}{2} + 20$

$\frac{y \cdot - 1}{16} + \frac{5}{2} = 19$

$x = \frac{y}{2} + 20$

Move $- 1$ to the left of $y$ .

$\frac{- 1 \cdot y}{16} + \frac{5}{2} = 19$

$x = \frac{y}{2} + 20$

Move the negative in front of the fraction.

$- \frac{y}{16} + \frac{5}{2} = 19$

$x = \frac{y}{2} + 20$

$- \frac{y}{16} + \frac{5}{2} = 19$

$x = \frac{y}{2} + 20$

$- \frac{y}{16} + \frac{5}{2} = 19$

$x = \frac{y}{2} + 20$

$- \frac{y}{16} + \frac{5}{2} = 19$

$x = \frac{y}{2} + 20$

$- \frac{y}{16} + \frac{5}{2} = 19$

$x = \frac{y}{2} + 20$

Solve for $y$ in $- \frac{y}{16} + \frac{5}{2} = 19$ .

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

Subtract $\frac{5}{2}$ from both sides of the equation.

$- \frac{y}{16} = 19 - \frac{5}{2}$

$x = \frac{y}{2} + 20$

To write $19$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{y}{16} = 19 \cdot \frac{2}{2} - \frac{5}{2}$

$x = \frac{y}{2} + 20$

Combine $19$ and $\frac{2}{2}$ .

$- \frac{y}{16} = \frac{19 \cdot 2}{2} - \frac{5}{2}$

$x = \frac{y}{2} + 20$

Combine the numerators over the common denominator.

$- \frac{y}{16} = \frac{19 \cdot 2 - 5}{2}$

$x = \frac{y}{2} + 20$

Simplify the numerator.

Multiply $19$ by $2$ .

$- \frac{y}{16} = \frac{38 - 5}{2}$

$x = \frac{y}{2} + 20$

Subtract $5$ from $38$ .

$- \frac{y}{16} = \frac{33}{2}$

$x = \frac{y}{2} + 20$

$- \frac{y}{16} = \frac{33}{2}$

$x = \frac{y}{2} + 20$

$- \frac{y}{16} = \frac{33}{2}$

$x = \frac{y}{2} + 20$

Multiply both sides of the equation by $- 16$ .

$- 16 (- \frac{y}{16}) = - 16 (\frac{33}{2})$

$x = \frac{y}{2} + 20$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 16 (- \frac{y}{16})$ .

Cancel the common factor of $16$ .

Move the leading negative in $- \frac{y}{16}$ into the numerator.

$- 16 \frac{- y}{16} = - 16 (\frac{33}{2})$

$x = \frac{y}{2} + 20$

Factor $16$ out of $- 16$ .

$16 (- 1) (\frac{- y}{16}) = - 16 (\frac{33}{2})$

$x = \frac{y}{2} + 20$

Cancel the common factor.

$16 \cdot (- 1 \frac{- y}{16}) = - 16 (\frac{33}{2})$

$x = \frac{y}{2} + 20$

Rewrite the expression.

$y = - 16 (\frac{33}{2})$

$x = \frac{y}{2} + 20$

$y = - 16 (\frac{33}{2})$

$x = \frac{y}{2} + 20$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 y = - 16 (\frac{33}{2})$

$x = \frac{y}{2} + 20$

Multiply $y$ by $1$ .

$y = - 16 (\frac{33}{2})$

$x = \frac{y}{2} + 20$

$y = - 16 (\frac{33}{2})$

$x = \frac{y}{2} + 20$

$y = - 16 (\frac{33}{2})$

$x = \frac{y}{2} + 20$

$y = - 16 (\frac{33}{2})$

$x = \frac{y}{2} + 20$

Simplify the right side.

Simplify $- 16 (\frac{33}{2})$ .

Cancel the common factor of $2$ .

Factor $2$ out of $- 16$ .

$y = 2 (- 8) (\frac{33}{2})$

$x = \frac{y}{2} + 20$

Cancel the common factor.

$y = 2 \cdot (- 8 (\frac{33}{2}))$

$x = \frac{y}{2} + 20$

Rewrite the expression.

$y = - 8 \cdot 33$

$x = \frac{y}{2} + 20$

$y = - 8 \cdot 33$

$x = \frac{y}{2} + 20$

Multiply $- 8$ by $33$ .

$y = - 264$

$x = \frac{y}{2} + 20$

$y = - 264$

$x = \frac{y}{2} + 20$

$y = - 264$

$x = \frac{y}{2} + 20$

$y = - 264$

$x = \frac{y}{2} + 20$

$y = - 264$

$x = \frac{y}{2} + 20$

Replace all occurrences of $y$ with $- 264$ in each equation.

Replace all occurrences of $y$ in $x = \frac{y}{2} + 20$ with $- 264$ .

$x = \frac{- 264}{2} + 20$

$y = - 264$

Simplify the right side.

Simplify $\frac{- 264}{2} + 20$ .

Divide $- 264$ by $2$ .

$x = - 132 + 20$

$y = - 264$

Add $- 132$ and $20$ .

$x = - 112$

$y = - 264$

$x = - 112$

$y = - 264$

$x = - 112$

$y = - 264$

$x = - 112$

$y = - 264$

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

$(- 112, - 264)$

The result can be shown in multiple forms.

Point Form:

$(- 112, - 264)$

Equation Form:

$x = - 112, y = - 264$

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