Solve by Substitution 15x-10y=-1 , 5y=1+10x

$15 x - 10 y = - 1$ , $5 y = 1 + 10 x$

Step 1

Divide each term in $5 y = 1 + 10 x$ by $5$ and simplify.

Divide each term in $5 y = 1 + 10 x$ by $5$ .

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

$15 x - 10 y = - 1$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

$15 x - 10 y = - 1$

Divide $y$ by $1$ .

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

$15 x - 10 y = - 1$

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

$15 x - 10 y = - 1$

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

$15 x - 10 y = - 1$

Simplify the right side.

Cancel the common factor of $10$ and $5$ .

Factor $5$ out of $10 x$ .

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

$15 x - 10 y = - 1$

Cancel the common factors.

Factor $5$ out of $5$ .

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

$15 x - 10 y = - 1$

Cancel the common factor.

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

$15 x - 10 y = - 1$

Rewrite the expression.

$y = \frac{1}{5} + \frac{2 x}{1}$

$15 x - 10 y = - 1$

Divide $2 x$ by $1$ .

$y = \frac{1}{5} + 2 x$

$15 x - 10 y = - 1$

$y = \frac{1}{5} + 2 x$

$15 x - 10 y = - 1$

$y = \frac{1}{5} + 2 x$

$15 x - 10 y = - 1$

$y = \frac{1}{5} + 2 x$

$15 x - 10 y = - 1$

$y = \frac{1}{5} + 2 x$

$15 x - 10 y = - 1$

Step 2

Replace all occurrences of $y$ with $\frac{1}{5} + 2 x$ in each equation.

Replace all occurrences of $y$ in $15 x - 10 y = - 1$ with $\frac{1}{5} + 2 x$ .

$15 x - 10 (\frac{1}{5} + 2 x) = - 1$

$y = \frac{1}{5} + 2 x$

Simplify the left side.

Simplify $15 x - 10 (\frac{1}{5} + 2 x)$ .

Simplify each term.

Apply the distributive property.

$15 x - 10 (\frac{1}{5}) - 10 (2 x) = - 1$

$y = \frac{1}{5} + 2 x$

Cancel the common factor of $5$ .

Factor $5$ out of $- 10$ .

$15 x + 5 (- 2) (\frac{1}{5}) - 10 (2 x) = - 1$

$y = \frac{1}{5} + 2 x$

Cancel the common factor.

$15 x + 5 \cdot (- 2 (\frac{1}{5})) - 10 (2 x) = - 1$

$y = \frac{1}{5} + 2 x$

Rewrite the expression.

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

$y = \frac{1}{5} + 2 x$

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

$y = \frac{1}{5} + 2 x$

Multiply $2$ by $- 10$ .

$15 x - 2 - 20 x = - 1$

$y = \frac{1}{5} + 2 x$

$15 x - 2 - 20 x = - 1$

$y = \frac{1}{5} + 2 x$

Subtract $20 x$ from $15 x$ .

$- 5 x - 2 = - 1$

$y = \frac{1}{5} + 2 x$

$- 5 x - 2 = - 1$

$y = \frac{1}{5} + 2 x$

$- 5 x - 2 = - 1$

$y = \frac{1}{5} + 2 x$

$- 5 x - 2 = - 1$

$y = \frac{1}{5} + 2 x$

Step 3

Solve for $x$ in $- 5 x - 2 = - 1$ .

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

Add $2$ to both sides of the equation.

$- 5 x = - 1 + 2$

$y = \frac{1}{5} + 2 x$

Add $- 1$ and $2$ .

$- 5 x = 1$

$y = \frac{1}{5} + 2 x$

$- 5 x = 1$

$y = \frac{1}{5} + 2 x$

Divide each term in $- 5 x = 1$ by $- 5$ and simplify.

Divide each term in $- 5 x = 1$ by $- 5$ .

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

$y = \frac{1}{5} + 2 x$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

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

$y = \frac{1}{5} + 2 x$

Divide $x$ by $1$ .

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

$y = \frac{1}{5} + 2 x$

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

$y = \frac{1}{5} + 2 x$

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

$y = \frac{1}{5} + 2 x$

Simplify the right side.

Move the negative in front of the fraction.

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

$y = \frac{1}{5} + 2 x$

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

$y = \frac{1}{5} + 2 x$

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

$y = \frac{1}{5} + 2 x$

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

$y = \frac{1}{5} + 2 x$

Step 4

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

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

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

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

Simplify the right side.

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

Simplify each term.

Multiply $2 (- \frac{1}{5})$ .

Multiply $- 1$ by $2$ .

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

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

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

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

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

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

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

Move the negative in front of the fraction.

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

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

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

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

Combine fractions.

Combine the numerators over the common denominator.

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

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

Simplify the expression.

Subtract $2$ from $1$ .

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

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

Move the negative in front of the fraction.

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

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

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

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

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

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

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

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

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

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

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

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

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

Solve by Substitution 15x-10y=-1 , 5y=1+10x

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