Solve by Substitution -2x=27-5y , 4y=20+2x

$- 2 x = 27 - 5 y$ , $4 y = 20 + 2 x$

Divide each term by $- 2$ and simplify.

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Divide each term in $- 2 x = 27 - 5 y$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{27}{- 2} + \frac{- 5 y}{- 2}$

$4 y = 20 + 2 x$

Cancel the common factor of $- 2$ .

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Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{27}{- 2} + \frac{- 5 y}{- 2}$

$4 y = 20 + 2 x$

Divide $x$ by $1$ .

$x = \frac{27}{- 2} + \frac{- 5 y}{- 2}$

$4 y = 20 + 2 x$

$x = \frac{27}{- 2} + \frac{- 5 y}{- 2}$

$4 y = 20 + 2 x$

Simplify each term.

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Move the negative in front of the fraction.

$x = - \frac{27}{2} + \frac{- 5 y}{- 2}$

$4 y = 20 + 2 x$

Dividing two negative values results in a positive value.

$x = - \frac{27}{2} + \frac{5 y}{2}$

$4 y = 20 + 2 x$

$x = - \frac{27}{2} + \frac{5 y}{2}$

$4 y = 20 + 2 x$

$x = - \frac{27}{2} + \frac{5 y}{2}$

$4 y = 20 + 2 x$

Replace all occurrences of $x$ with $- \frac{27}{2} + \frac{5 y}{2}$ in each equation.

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Replace all occurrences of $x$ in $4 y = 20 + 2 x$ with $- \frac{27}{2} + \frac{5 y}{2}$ .

$4 y = 20 + 2 (- \frac{27}{2} + \frac{5 y}{2})$

$x = - \frac{27}{2} + \frac{5 y}{2}$

Simplify $20 + 2 (- \frac{27}{2} + \frac{5 y}{2})$ .

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Simplify each term.

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Apply the distributive property.

$4 y = 20 + 2 (- \frac{27}{2}) + 2 (\frac{5 y}{2})$

$x = - \frac{27}{2} + \frac{5 y}{2}$

Cancel the common factor of $2$ .

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Move the leading negative in $- \frac{27}{2}$ into the numerator.

$4 y = 20 + 2 (\frac{- 27}{2}) + 2 (\frac{5 y}{2})$

$x = - \frac{27}{2} + \frac{5 y}{2}$

Cancel the common factor.

$4 y = 20 + 2 (\frac{- 27}{2}) + 2 (\frac{5 y}{2})$

$x = - \frac{27}{2} + \frac{5 y}{2}$

Rewrite the expression.

$4 y = 20 - 27 + 2 (\frac{5 y}{2})$

$x = - \frac{27}{2} + \frac{5 y}{2}$

$4 y = 20 - 27 + 2 (\frac{5 y}{2})$

$x = - \frac{27}{2} + \frac{5 y}{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$4 y = 20 - 27 + 2 (\frac{5 y}{2})$

$x = - \frac{27}{2} + \frac{5 y}{2}$

Rewrite the expression.

$4 y = 20 - 27 + 5 y$

$x = - \frac{27}{2} + \frac{5 y}{2}$

$4 y = 20 - 27 + 5 y$

$x = - \frac{27}{2} + \frac{5 y}{2}$

$4 y = 20 - 27 + 5 y$

$x = - \frac{27}{2} + \frac{5 y}{2}$

Subtract $27$ from $20$ .

$4 y = - 7 + 5 y$

$x = - \frac{27}{2} + \frac{5 y}{2}$

$4 y = - 7 + 5 y$

$x = - \frac{27}{2} + \frac{5 y}{2}$

$4 y = - 7 + 5 y$

$x = - \frac{27}{2} + \frac{5 y}{2}$

Solve for $y$ in the first equation.

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

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Subtract $5 y$ from both sides of the equation.

$4 y - 5 y = - 7$

$x = - \frac{27}{2} + \frac{5 y}{2}$

Subtract $5 y$ from $4 y$ .

$- y = - 7$

$x = - \frac{27}{2} + \frac{5 y}{2}$

$- y = - 7$

$x = - \frac{27}{2} + \frac{5 y}{2}$

Multiply each term in $- y = - 7$ by $- 1$

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Multiply each term in $- y = - 7$ by $- 1$ .

$(- y) \cdot - 1 = (- 7) \cdot - 1$

$x = - \frac{27}{2} + \frac{5 y}{2}$

Multiply $(- y) \cdot - 1$ .

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Multiply $- 1$ by $- 1$ .

$1 y = (- 7) \cdot - 1$

$x = - \frac{27}{2} + \frac{5 y}{2}$

Multiply $y$ by $1$ .

$y = (- 7) \cdot - 1$

$x = - \frac{27}{2} + \frac{5 y}{2}$

$y = (- 7) \cdot - 1$

$x = - \frac{27}{2} + \frac{5 y}{2}$

Multiply $- 7$ by $- 1$ .

$y = 7$

$x = - \frac{27}{2} + \frac{5 y}{2}$

$y = 7$

$x = - \frac{27}{2} + \frac{5 y}{2}$

$y = 7$

$x = - \frac{27}{2} + \frac{5 y}{2}$

Replace all occurrences of $y$ with $7$ in each equation.

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Replace all occurrences of $y$ in $x = - \frac{27}{2} + \frac{5 y}{2}$ with $7$ .

$x = - \frac{27}{2} + \frac{5 (7)}{2}$

$y = 7$

Simplify $- \frac{27}{2} + \frac{5 (7)}{2}$ .

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Combine the numerators over the common denominator.

$x = \frac{- 27 + 5 (7)}{2}$

$y = 7$

Simplify the expression.

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Multiply $5$ by $7$ .

$x = \frac{- 27 + 35}{2}$

$y = 7$

Add $- 27$ and $35$ .

$x = \frac{8}{2}$

$y = 7$

Divide $8$ by $2$ .

$x = 4$

$y = 7$

$x = 4$

$y = 7$

$x = 4$

$y = 7$

$x = 4$

$y = 7$

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

$(4, 7)$

The result can be shown in multiple forms.

Point Form:

$(4, 7)$

Equation Form:

$x = 4, y = 7$

Solve by Substitution -2x=27-5y , 4y=20+2x