Solve by Substitution 15x-20y=1 , 10y=1+15x

$15 x - 20 y = 1$ , $10 y = 1 + 15 x$

Step 1

Divide each term in $10 y = 1 + 15 x$ by $10$ and simplify.

Divide each term in $10 y = 1 + 15 x$ by $10$ .

$\frac{10 y}{10} = \frac{1}{10} + \frac{15 x}{10}$

$15 x - 20 y = 1$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 y}{10} = \frac{1}{10} + \frac{15 x}{10}$

$15 x - 20 y = 1$

Divide $y$ by $1$ .

$y = \frac{1}{10} + \frac{15 x}{10}$

$15 x - 20 y = 1$

$y = \frac{1}{10} + \frac{15 x}{10}$

$15 x - 20 y = 1$

$y = \frac{1}{10} + \frac{15 x}{10}$

$15 x - 20 y = 1$

Simplify the right side.

Cancel the common factor of $15$ and $10$ .

Factor $5$ out of $15 x$ .

$y = \frac{1}{10} + \frac{5 (3 x)}{10}$

$15 x - 20 y = 1$

Cancel the common factors.

Factor $5$ out of $10$ .

$y = \frac{1}{10} + \frac{5 (3 x)}{5 (2)}$

$15 x - 20 y = 1$

Cancel the common factor.

$y = \frac{1}{10} + \frac{5 (3 x)}{5 \cdot 2}$

$15 x - 20 y = 1$

Rewrite the expression.

$y = \frac{1}{10} + \frac{3 x}{2}$

$15 x - 20 y = 1$

$y = \frac{1}{10} + \frac{3 x}{2}$

$15 x - 20 y = 1$

$y = \frac{1}{10} + \frac{3 x}{2}$

$15 x - 20 y = 1$

$y = \frac{1}{10} + \frac{3 x}{2}$

$15 x - 20 y = 1$

$y = \frac{1}{10} + \frac{3 x}{2}$

$15 x - 20 y = 1$

Step 2

Replace all occurrences of $y$ with $\frac{1}{10} + \frac{3 x}{2}$ in each equation.

Replace all occurrences of $y$ in $15 x - 20 y = 1$ with $\frac{1}{10} + \frac{3 x}{2}$ .

$15 x - 20 (\frac{1}{10} + \frac{3 x}{2}) = 1$

$y = \frac{1}{10} + \frac{3 x}{2}$

Simplify the left side.

Simplify $15 x - 20 (\frac{1}{10} + \frac{3 x}{2})$ .

Simplify each term.

Apply the distributive property.

$15 x - 20 (\frac{1}{10}) - 20 \frac{3 x}{2} = 1$

$y = \frac{1}{10} + \frac{3 x}{2}$

Cancel the common factor of $10$ .

Factor $10$ out of $- 20$ .

$15 x + 10 (- 2) (\frac{1}{10}) - 20 \frac{3 x}{2} = 1$

$y = \frac{1}{10} + \frac{3 x}{2}$

Cancel the common factor.

$15 x + 10 \cdot (- 2 (\frac{1}{10})) - 20 \frac{3 x}{2} = 1$

$y = \frac{1}{10} + \frac{3 x}{2}$

Rewrite the expression.

$15 x - 2 - 20 \frac{3 x}{2} = 1$

$y = \frac{1}{10} + \frac{3 x}{2}$

$15 x - 2 - 20 \frac{3 x}{2} = 1$

$y = \frac{1}{10} + \frac{3 x}{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $- 20$ .

$15 x - 2 + 2 (- 10) (\frac{3 x}{2}) = 1$

$y = \frac{1}{10} + \frac{3 x}{2}$

Cancel the common factor.

$15 x - 2 + 2 \cdot (- 10 \frac{3 x}{2}) = 1$

$y = \frac{1}{10} + \frac{3 x}{2}$

Rewrite the expression.

$15 x - 2 - 10 (3 x) = 1$

$y = \frac{1}{10} + \frac{3 x}{2}$

$15 x - 2 - 10 (3 x) = 1$

$y = \frac{1}{10} + \frac{3 x}{2}$

Multiply $3$ by $- 10$ .

$15 x - 2 - 30 x = 1$

$y = \frac{1}{10} + \frac{3 x}{2}$

$15 x - 2 - 30 x = 1$

$y = \frac{1}{10} + \frac{3 x}{2}$

Subtract $30 x$ from $15 x$ .

$- 15 x - 2 = 1$

$y = \frac{1}{10} + \frac{3 x}{2}$

$- 15 x - 2 = 1$

$y = \frac{1}{10} + \frac{3 x}{2}$

$- 15 x - 2 = 1$

$y = \frac{1}{10} + \frac{3 x}{2}$

$- 15 x - 2 = 1$

$y = \frac{1}{10} + \frac{3 x}{2}$

Step 3

Solve for $x$ in $- 15 x - 2 = 1$ .

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

Add $2$ to both sides of the equation.

$- 15 x = 1 + 2$

$y = \frac{1}{10} + \frac{3 x}{2}$

Add $1$ and $2$ .

$- 15 x = 3$

$y = \frac{1}{10} + \frac{3 x}{2}$

$- 15 x = 3$

$y = \frac{1}{10} + \frac{3 x}{2}$

Divide each term in $- 15 x = 3$ by $- 15$ and simplify.

Divide each term in $- 15 x = 3$ by $- 15$ .

$\frac{- 15 x}{- 15} = \frac{3}{- 15}$

$y = \frac{1}{10} + \frac{3 x}{2}$

Simplify the left side.

Cancel the common factor of $- 15$ .

Cancel the common factor.

$\frac{- 15 x}{- 15} = \frac{3}{- 15}$

$y = \frac{1}{10} + \frac{3 x}{2}$

Divide $x$ by $1$ .

$x = \frac{3}{- 15}$

$y = \frac{1}{10} + \frac{3 x}{2}$

$x = \frac{3}{- 15}$

$y = \frac{1}{10} + \frac{3 x}{2}$

$x = \frac{3}{- 15}$

$y = \frac{1}{10} + \frac{3 x}{2}$

Simplify the right side.

Cancel the common factor of $3$ and $- 15$ .

Factor $3$ out of $3$ .

$x = \frac{3 (1)}{- 15}$

$y = \frac{1}{10} + \frac{3 x}{2}$

Cancel the common factors.

Factor $3$ out of $- 15$ .

$x = \frac{3 \cdot 1}{3 \cdot - 5}$

$y = \frac{1}{10} + \frac{3 x}{2}$

Cancel the common factor.

$x = \frac{3 \cdot 1}{3 \cdot - 5}$

$y = \frac{1}{10} + \frac{3 x}{2}$

Rewrite the expression.

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

$y = \frac{1}{10} + \frac{3 x}{2}$

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

$y = \frac{1}{10} + \frac{3 x}{2}$

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

$y = \frac{1}{10} + \frac{3 x}{2}$

Move the negative in front of the fraction.

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

$y = \frac{1}{10} + \frac{3 x}{2}$

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

$y = \frac{1}{10} + \frac{3 x}{2}$

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

$y = \frac{1}{10} + \frac{3 x}{2}$

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

$y = \frac{1}{10} + \frac{3 x}{2}$

Step 4

Replace all occurrences of $x$ with $- \frac{1}{5}$ in each equation.

Replace all occurrences of $x$ in $y = \frac{1}{10} + \frac{3 x}{2}$ with $- \frac{1}{5}$ .

$y = \frac{1}{10} + \frac{3 (- \frac{1}{5})}{2}$

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

Simplify the right side.

Simplify $\frac{1}{10} + \frac{3 (- \frac{1}{5})}{2}$ .

Simplify each term.

Simplify the numerator.

Multiply $- 1$ by $3$ .

$y = \frac{1}{10} + \frac{- 3 (\frac{1}{5})}{2}$

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

Combine $- 3$ and $\frac{1}{5}$ .

$y = \frac{1}{10} + \frac{\frac{- 3}{5}}{2}$

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

$y = \frac{1}{10} + \frac{\frac{- 3}{5}}{2}$

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

Move the negative in front of the fraction.

$y = \frac{1}{10} + \frac{- \frac{3}{5}}{2}$

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

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{1}{10} - \frac{3}{5} \cdot \frac{1}{2}$

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

Multiply $- \frac{3}{5} \cdot \frac{1}{2}$ .

Multiply $\frac{1}{2}$ by $\frac{3}{5}$ .

$y = \frac{1}{10} - \frac{3}{2 \cdot 5}$

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

Multiply $2$ by $5$ .

$y = \frac{1}{10} - \frac{3}{10}$

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

$y = \frac{1}{10} - \frac{3}{10}$

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

$y = \frac{1}{10} - \frac{3}{10}$

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

Simplify terms.

Combine the numerators over the common denominator.

$y = \frac{1 - 3}{10}$

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

Subtract $3$ from $1$ .

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

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

Cancel the common factor of $- 2$ and $10$ .

Factor $2$ out of $- 2$ .

$y = \frac{2 (- 1)}{10}$

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

Cancel the common factors.

Factor $2$ out of $10$ .

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

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

Cancel the common factor.

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

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

Rewrite the expression.

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

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

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

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

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

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

Move the negative in front of the fraction.

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

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

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

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

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

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

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

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

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

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

Step 5

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

$(- \frac{1}{5}, - \frac{1}{5})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- \frac{1}{5}, - \frac{1}{5})$

Equation Form:

$x = - \frac{1}{5}, y = - \frac{1}{5}$

Step 7

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