Solve the System of Equations 2x+7y=1 -(5x)/8+y/4=17/8

$2 x + 7 y = 1$ $- \frac{5 x}{8} + \frac{y}{4} = \frac{17}{8}$

Solve for $x$ in $2 x + 7 y = 1$ .

Subtract $7 y$ from both sides of the equation.

$2 x = 1 - 7 y$

$- \frac{5 x}{8} + \frac{y}{4} = \frac{17}{8}$

Divide each term in $2 x = 1 - 7 y$ by $2$ and simplify.

Divide each term in $2 x = 1 - 7 y$ by $2$ .

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

$- \frac{5 x}{8} + \frac{y}{4} = \frac{17}{8}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

$- \frac{5 x}{8} + \frac{y}{4} = \frac{17}{8}$

Divide $x$ by $1$ .

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

$- \frac{5 x}{8} + \frac{y}{4} = \frac{17}{8}$

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

$- \frac{5 x}{8} + \frac{y}{4} = \frac{17}{8}$

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

$- \frac{5 x}{8} + \frac{y}{4} = \frac{17}{8}$

Simplify the right side.

Move the negative in front of the fraction.

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

$- \frac{5 x}{8} + \frac{y}{4} = \frac{17}{8}$

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

$- \frac{5 x}{8} + \frac{y}{4} = \frac{17}{8}$

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

$- \frac{5 x}{8} + \frac{y}{4} = \frac{17}{8}$

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

$- \frac{5 x}{8} + \frac{y}{4} = \frac{17}{8}$

Replace all occurrences of $x$ with $\frac{1}{2} - \frac{7 y}{2}$ in each equation.

Replace all occurrences of $x$ in $- \frac{5 x}{8} + \frac{y}{4} = \frac{17}{8}$ with $\frac{1}{2} - \frac{7 y}{2}$ .

$- \frac{5 (\frac{1}{2} - \frac{7 y}{2})}{8} + \frac{y}{4} = \frac{17}{8}$

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

Simplify the left side.

Simplify $- \frac{5 (\frac{1}{2} - \frac{7 y}{2})}{8} + \frac{y}{4}$ .

Simplify each term.

Combine the numerators over the common denominator.

$- \frac{5 (\frac{1 - 7 y}{2})}{8} + \frac{y}{4} = \frac{17}{8}$

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

Combine $5$ and $\frac{1 - 7 y}{2}$ .

$- \frac{\frac{5 (1 - 7 y)}{2}}{8} + \frac{y}{4} = \frac{17}{8}$

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

Multiply the numerator by the reciprocal of the denominator.

$- (\frac{5 (1 - 7 y)}{2} \cdot \frac{1}{8}) + \frac{y}{4} = \frac{17}{8}$

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

Multiply $\frac{5 (1 - 7 y)}{2} \cdot \frac{1}{8}$ .

Multiply $\frac{5 (1 - 7 y)}{2}$ by $\frac{1}{8}$ .

$- \frac{5 (1 - 7 y)}{2 \cdot 8} + \frac{y}{4} = \frac{17}{8}$

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

Multiply $2$ by $8$ .

$- \frac{5 (1 - 7 y)}{16} + \frac{y}{4} = \frac{17}{8}$

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

$- \frac{5 (1 - 7 y)}{16} + \frac{y}{4} = \frac{17}{8}$

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

$- \frac{5 (1 - 7 y)}{16} + \frac{y}{4} = \frac{17}{8}$

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

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

$- \frac{5 (1 - 7 y)}{16} + \frac{y}{4} \cdot \frac{4}{4} = \frac{17}{8}$

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

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

Multiply $\frac{y}{4}$ by $\frac{4}{4}$ .

$- \frac{5 (1 - 7 y)}{16} + \frac{y \cdot 4}{4 \cdot 4} = \frac{17}{8}$

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

Multiply $4$ by $4$ .

$- \frac{5 (1 - 7 y)}{16} + \frac{y \cdot 4}{16} = \frac{17}{8}$

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

$- \frac{5 (1 - 7 y)}{16} + \frac{y \cdot 4}{16} = \frac{17}{8}$

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

Combine the numerators over the common denominator.

$\frac{- 5 (1 - 7 y) + y \cdot 4}{16} = \frac{17}{8}$

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

Simplify the numerator.

Apply the distributive property.

$\frac{- 5 \cdot 1 - 5 (- 7 y) + y \cdot 4}{16} = \frac{17}{8}$

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

Multiply $- 5$ by $1$ .

$\frac{- 5 - 5 (- 7 y) + y \cdot 4}{16} = \frac{17}{8}$

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

Multiply $- 7$ by $- 5$ .

$\frac{- 5 + 35 y + y \cdot 4}{16} = \frac{17}{8}$

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

Move $4$ to the left of $y$ .

$\frac{- 5 + 35 y + 4 \cdot y}{16} = \frac{17}{8}$

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

Add $35 y$ and $4 y$ .

$\frac{- 5 + 39 y}{16} = \frac{17}{8}$

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

$\frac{- 5 + 39 y}{16} = \frac{17}{8}$

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

Simplify with factoring out.

Rewrite $- 5$ as $- 1 (5)$ .

$\frac{- 1 \cdot 5 + 39 y}{16} = \frac{17}{8}$

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

Factor $- 1$ out of $39 y$ .

$\frac{- 1 \cdot 5 - (- 39 y)}{16} = \frac{17}{8}$

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

Factor $- 1$ out of $- 1 (5) - (- 39 y)$ .

$\frac{- 1 (5 - 39 y)}{16} = \frac{17}{8}$

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

Move the negative in front of the fraction.

$- \frac{5 - 39 y}{16} = \frac{17}{8}$

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

$- \frac{5 - 39 y}{16} = \frac{17}{8}$

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

$- \frac{5 - 39 y}{16} = \frac{17}{8}$

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

$- \frac{5 - 39 y}{16} = \frac{17}{8}$

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

$- \frac{5 - 39 y}{16} = \frac{17}{8}$

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

Solve for $y$ in $- \frac{5 - 39 y}{16} = \frac{17}{8}$ .

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

$- 16 (- \frac{5 - 39 y}{16}) = - 16 (\frac{17}{8})$

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 16 (- \frac{5 - 39 y}{16})$ .

Cancel the common factor of $16$ .

Move the leading negative in $- \frac{5 - 39 y}{16}$ into the numerator.

$- 16 \frac{- (5 - 39 y)}{16} = - 16 (\frac{17}{8})$

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

Factor $16$ out of $- 16$ .

$16 (- 1) (\frac{- (5 - 39 y)}{16}) = - 16 (\frac{17}{8})$

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

Cancel the common factor.

$16 \cdot (- 1 \frac{- (5 - 39 y)}{16}) = - 16 (\frac{17}{8})$

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

Rewrite the expression.

$5 - 39 y = - 16 (\frac{17}{8})$

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

$5 - 39 y = - 16 (\frac{17}{8})$

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

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (5 - 39 y) = - 16 (\frac{17}{8})$

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

Multiply $5 - 39 y$ by $1$ .

$5 - 39 y = - 16 (\frac{17}{8})$

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

$5 - 39 y = - 16 (\frac{17}{8})$

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

$5 - 39 y = - 16 (\frac{17}{8})$

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

$5 - 39 y = - 16 (\frac{17}{8})$

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

Simplify the right side.

Simplify $- 16 (\frac{17}{8})$ .

Cancel the common factor of $8$ .

Factor $8$ out of $- 16$ .

$5 - 39 y = 8 (- 2) (\frac{17}{8})$

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

Cancel the common factor.

$5 - 39 y = 8 \cdot (- 2 (\frac{17}{8}))$

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

Rewrite the expression.

$5 - 39 y = - 2 \cdot 17$

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

$5 - 39 y = - 2 \cdot 17$

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

Multiply $- 2$ by $17$ .

$5 - 39 y = - 34$

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

$5 - 39 y = - 34$

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

$5 - 39 y = - 34$

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

$5 - 39 y = - 34$

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

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

Subtract $5$ from both sides of the equation.

$- 39 y = - 34 - 5$

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

Subtract $5$ from $- 34$ .

$- 39 y = - 39$

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

$- 39 y = - 39$

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

Divide each term in $- 39 y = - 39$ by $- 39$ and simplify.

Divide each term in $- 39 y = - 39$ by $- 39$ .

$\frac{- 39 y}{- 39} = \frac{- 39}{- 39}$

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

Simplify the left side.

Cancel the common factor of $- 39$ .

Cancel the common factor.

$\frac{- 39 y}{- 39} = \frac{- 39}{- 39}$

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

Divide $y$ by $1$ .

$y = \frac{- 39}{- 39}$

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

$y = \frac{- 39}{- 39}$

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

$y = \frac{- 39}{- 39}$

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

Simplify the right side.

Divide $- 39$ by $- 39$ .

$y = 1$

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

$y = 1$

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

$y = 1$

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

$y = 1$

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

Replace all occurrences of $y$ with $1$ in each equation.

Replace all occurrences of $y$ in $x = \frac{1}{2} - \frac{7 y}{2}$ with $1$ .

$x = \frac{1}{2} - \frac{7 (1)}{2}$

$y = 1$

Simplify the right side.

Simplify $\frac{1}{2} - \frac{7 (1)}{2}$ .

Combine the numerators over the common denominator.

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

$y = 1$

Simplify the expression.

Multiply $- 7$ by $1$ .

$x = \frac{1 - 7}{2}$

$y = 1$

Subtract $7$ from $1$ .

$x = \frac{- 6}{2}$

$y = 1$

Divide $- 6$ by $2$ .

$x = - 3$

$y = 1$

$x = - 3$

$y = 1$

$x = - 3$

$y = 1$

$x = - 3$

$y = 1$

$x = - 3$

$y = 1$

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

$(- 3, 1)$

The result can be shown in multiple forms.

Point Form:

$(- 3, 1)$

Equation Form:

$x = - 3, y = 1$

Solve the System of Equations 2x+7y=1 -(5x)/8+y/4=17/8

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