Solve the System of Equations 4x+2y=1 5x=y-18

$4 x + 2 y = 1$ $5 x = y - 18$

Divide each term in $5 x = y - 18$ by $5$ and simplify.

Divide each term in $5 x = y - 18$ by $5$ .

$\frac{5 x}{5} = \frac{y}{5} + \frac{- 18}{5}$

$4 x + 2 y = 1$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{y}{5} + \frac{- 18}{5}$

$4 x + 2 y = 1$

Divide $x$ by $1$ .

$x = \frac{y}{5} + \frac{- 18}{5}$

$4 x + 2 y = 1$

$x = \frac{y}{5} + \frac{- 18}{5}$

$4 x + 2 y = 1$

$x = \frac{y}{5} + \frac{- 18}{5}$

$4 x + 2 y = 1$

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{y}{5} - \frac{18}{5}$

$4 x + 2 y = 1$

$x = \frac{y}{5} - \frac{18}{5}$

$4 x + 2 y = 1$

$x = \frac{y}{5} - \frac{18}{5}$

$4 x + 2 y = 1$

Replace all occurrences of $x$ with $\frac{y}{5} - \frac{18}{5}$ in each equation.

Replace all occurrences of $x$ in $4 x + 2 y = 1$ with $\frac{y}{5} - \frac{18}{5}$ .

$4 (\frac{y}{5} - \frac{18}{5}) + 2 y = 1$

$x = \frac{y}{5} - \frac{18}{5}$

Simplify the left side.

Simplify $4 (\frac{y}{5} - \frac{18}{5}) + 2 y$ .

Simplify each term.

Apply the distributive property.

$4 (\frac{y}{5}) + 4 (- \frac{18}{5}) + 2 y = 1$

$x = \frac{y}{5} - \frac{18}{5}$

Combine $4$ and $\frac{y}{5}$ .

$\frac{4 y}{5} + 4 (- \frac{18}{5}) + 2 y = 1$

$x = \frac{y}{5} - \frac{18}{5}$

Multiply $4 (- \frac{18}{5})$ .

Multiply $- 1$ by $4$ .

$\frac{4 y}{5} - 4 (\frac{18}{5}) + 2 y = 1$

$x = \frac{y}{5} - \frac{18}{5}$

Combine $- 4$ and $\frac{18}{5}$ .

$\frac{4 y}{5} + \frac{- 4 \cdot 18}{5} + 2 y = 1$

$x = \frac{y}{5} - \frac{18}{5}$

Multiply $- 4$ by $18$ .

$\frac{4 y}{5} + \frac{- 72}{5} + 2 y = 1$

$x = \frac{y}{5} - \frac{18}{5}$

$\frac{4 y}{5} + \frac{- 72}{5} + 2 y = 1$

$x = \frac{y}{5} - \frac{18}{5}$

Move the negative in front of the fraction.

$\frac{4 y}{5} - \frac{72}{5} + 2 y = 1$

$x = \frac{y}{5} - \frac{18}{5}$

$\frac{4 y}{5} - \frac{72}{5} + 2 y = 1$

$x = \frac{y}{5} - \frac{18}{5}$

To write $2 y$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{4 y}{5} + 2 y \cdot \frac{5}{5} - \frac{72}{5} = 1$

$x = \frac{y}{5} - \frac{18}{5}$

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

$\frac{4 y}{5} + \frac{2 y \cdot 5}{5} - \frac{72}{5} = 1$

$x = \frac{y}{5} - \frac{18}{5}$

Combine the numerators over the common denominator.

$\frac{4 y + 2 y \cdot 5}{5} - \frac{72}{5} = 1$

$x = \frac{y}{5} - \frac{18}{5}$

Combine the numerators over the common denominator.

$\frac{4 y + 2 y \cdot 5 - 72}{5} = 1$

$x = \frac{y}{5} - \frac{18}{5}$

Multiply $5$ by $2$ .

$\frac{4 y + 10 y - 72}{5} = 1$

$x = \frac{y}{5} - \frac{18}{5}$

Add $4 y$ and $10 y$ .

$\frac{14 y - 72}{5} = 1$

$x = \frac{y}{5} - \frac{18}{5}$

Factor $2$ out of $14 y - 72$ .

Factor $2$ out of $14 y$ .

$\frac{2 (7 y) - 72}{5} = 1$

$x = \frac{y}{5} - \frac{18}{5}$

Factor $2$ out of $- 72$ .

$\frac{2 (7 y) + 2 (- 36)}{5} = 1$

$x = \frac{y}{5} - \frac{18}{5}$

Factor $2$ out of $2 (7 y) + 2 (- 36)$ .

$\frac{2 (7 y - 36)}{5} = 1$

$x = \frac{y}{5} - \frac{18}{5}$

$\frac{2 (7 y - 36)}{5} = 1$

$x = \frac{y}{5} - \frac{18}{5}$

$\frac{2 (7 y - 36)}{5} = 1$

$x = \frac{y}{5} - \frac{18}{5}$

$\frac{2 (7 y - 36)}{5} = 1$

$x = \frac{y}{5} - \frac{18}{5}$

$\frac{2 (7 y - 36)}{5} = 1$

$x = \frac{y}{5} - \frac{18}{5}$

Solve for $y$ in $\frac{2 (7 y - 36)}{5} = 1$ .

Multiply both sides by $5$ .

$\frac{2 (7 y - 36)}{5} \cdot 5 = 1 \cdot 5$

$x = \frac{y}{5} - \frac{18}{5}$

Simplify.

Simplify the left side.

Simplify $\frac{2 (7 y - 36)}{5} \cdot 5$ .

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{2 (7 y - 36)}{5} \cdot 5 = 1 \cdot 5$

$x = \frac{y}{5} - \frac{18}{5}$

Rewrite the expression.

$2 (7 y - 36) = 1 \cdot 5$

$x = \frac{y}{5} - \frac{18}{5}$

$2 (7 y - 36) = 1 \cdot 5$

$x = \frac{y}{5} - \frac{18}{5}$

Apply the distributive property.

$2 (7 y) + 2 \cdot - 36 = 1 \cdot 5$

$x = \frac{y}{5} - \frac{18}{5}$

Multiply.

Multiply $7$ by $2$ .

$14 y + 2 \cdot - 36 = 1 \cdot 5$

$x = \frac{y}{5} - \frac{18}{5}$

Multiply $2$ by $- 36$ .

$14 y - 72 = 1 \cdot 5$

$x = \frac{y}{5} - \frac{18}{5}$

$14 y - 72 = 1 \cdot 5$

$x = \frac{y}{5} - \frac{18}{5}$

$14 y - 72 = 1 \cdot 5$

$x = \frac{y}{5} - \frac{18}{5}$

$14 y - 72 = 1 \cdot 5$

$x = \frac{y}{5} - \frac{18}{5}$

Simplify the right side.

Multiply $5$ by $1$ .

$14 y - 72 = 5$

$x = \frac{y}{5} - \frac{18}{5}$

$14 y - 72 = 5$

$x = \frac{y}{5} - \frac{18}{5}$

$14 y - 72 = 5$

$x = \frac{y}{5} - \frac{18}{5}$

Solve for $y$ .

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

Add $72$ to both sides of the equation.

$14 y = 5 + 72$

$x = \frac{y}{5} - \frac{18}{5}$

Add $5$ and $72$ .

$14 y = 77$

$x = \frac{y}{5} - \frac{18}{5}$

$14 y = 77$

$x = \frac{y}{5} - \frac{18}{5}$

Divide each term in $14 y = 77$ by $14$ and simplify.

Divide each term in $14 y = 77$ by $14$ .

$\frac{14 y}{14} = \frac{77}{14}$

$x = \frac{y}{5} - \frac{18}{5}$

Simplify the left side.

Cancel the common factor of $14$ .

Cancel the common factor.

$\frac{14 y}{14} = \frac{77}{14}$

$x = \frac{y}{5} - \frac{18}{5}$

Divide $y$ by $1$ .

$y = \frac{77}{14}$

$x = \frac{y}{5} - \frac{18}{5}$

$y = \frac{77}{14}$

$x = \frac{y}{5} - \frac{18}{5}$

$y = \frac{77}{14}$

$x = \frac{y}{5} - \frac{18}{5}$

Simplify the right side.

Cancel the common factor of $77$ and $14$ .

Factor $7$ out of $77$ .

$y = \frac{7 (11)}{14}$

$x = \frac{y}{5} - \frac{18}{5}$

Cancel the common factors.

Factor $7$ out of $14$ .

$y = \frac{7 \cdot 11}{7 \cdot 2}$

$x = \frac{y}{5} - \frac{18}{5}$

Cancel the common factor.

$y = \frac{7 \cdot 11}{7 \cdot 2}$

$x = \frac{y}{5} - \frac{18}{5}$

Rewrite the expression.

$y = \frac{11}{2}$

$x = \frac{y}{5} - \frac{18}{5}$

$y = \frac{11}{2}$

$x = \frac{y}{5} - \frac{18}{5}$

$y = \frac{11}{2}$

$x = \frac{y}{5} - \frac{18}{5}$

$y = \frac{11}{2}$

$x = \frac{y}{5} - \frac{18}{5}$

$y = \frac{11}{2}$

$x = \frac{y}{5} - \frac{18}{5}$

$y = \frac{11}{2}$

$x = \frac{y}{5} - \frac{18}{5}$

$y = \frac{11}{2}$

$x = \frac{y}{5} - \frac{18}{5}$

Replace all occurrences of $y$ with $\frac{11}{2}$ in each equation.

Replace all occurrences of $y$ in $x = \frac{y}{5} - \frac{18}{5}$ with $\frac{11}{2}$ .

$x = \frac{\frac{11}{2}}{5} - \frac{18}{5}$

$y = \frac{11}{2}$

Simplify the right side.

Simplify $\frac{\frac{11}{2}}{5} - \frac{18}{5}$ .

Combine the numerators over the common denominator.

$x = \frac{\frac{11}{2} - 18}{5}$

$y = \frac{11}{2}$

To write $- 18$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = \frac{\frac{11}{2} - 18 \cdot \frac{2}{2}}{5}$

$y = \frac{11}{2}$

Combine $- 18$ and $\frac{2}{2}$ .

$x = \frac{\frac{11}{2} + \frac{- 18 \cdot 2}{2}}{5}$

$y = \frac{11}{2}$

Combine the numerators over the common denominator.

$x = \frac{\frac{11 - 18 \cdot 2}{2}}{5}$

$y = \frac{11}{2}$

Simplify the numerator.

Multiply $- 18$ by $2$ .

$x = \frac{\frac{11 - 36}{2}}{5}$

$y = \frac{11}{2}$

Subtract $36$ from $11$ .

$x = \frac{\frac{- 25}{2}}{5}$

$y = \frac{11}{2}$

$x = \frac{\frac{- 25}{2}}{5}$

$y = \frac{11}{2}$

Move the negative in front of the fraction.

$x = \frac{- \frac{25}{2}}{5}$

$y = \frac{11}{2}$

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{25}{2} \cdot \frac{1}{5}$

$y = \frac{11}{2}$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{25}{2}$ into the numerator.

$x = \frac{- 25}{2} \cdot \frac{1}{5}$

$y = \frac{11}{2}$

Factor $5$ out of $- 25$ .

$x = \frac{5 (- 5)}{2} \cdot \frac{1}{5}$

$y = \frac{11}{2}$

Cancel the common factor.

$x = \frac{5 \cdot - 5}{2} \cdot \frac{1}{5}$

$y = \frac{11}{2}$

Rewrite the expression.

$x = \frac{- 5}{2}$

$y = \frac{11}{2}$

$x = \frac{- 5}{2}$

$y = \frac{11}{2}$

Move the negative in front of the fraction.

$x = - \frac{5}{2}$

$y = \frac{11}{2}$

$x = - \frac{5}{2}$

$y = \frac{11}{2}$

$x = - \frac{5}{2}$

$y = \frac{11}{2}$

$x = - \frac{5}{2}$

$y = \frac{11}{2}$

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

$(- \frac{5}{2}, \frac{11}{2})$

The result can be shown in multiple forms.

Point Form:

$(- \frac{5}{2}, \frac{11}{2})$

Equation Form:

$x = - \frac{5}{2}, y = \frac{11}{2}$

Solve the System of Equations 4x+2y=1 5x=y-18

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