Solve by Substitution 15x-10y=-5 , 5y=2+5x

$15 x - 10 y = - 5$ , $5 y = 2 + 5 x$

Step 1

Divide each term in $5 y = 2 + 5 x$ by $5$ and simplify.

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

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

$15 x - 10 y = - 5$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

$15 x - 10 y = - 5$

Divide $y$ by $1$ .

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

$15 x - 10 y = - 5$

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

$15 x - 10 y = - 5$

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

$15 x - 10 y = - 5$

Simplify the right side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

$15 x - 10 y = - 5$

Divide $x$ by $1$ .

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

$15 x - 10 y = - 5$

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

$15 x - 10 y = - 5$

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

$15 x - 10 y = - 5$

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

$15 x - 10 y = - 5$

Step 2

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

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

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

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

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

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

Cancel the common factor of $5$ .

Factor $5$ out of $- 10$ .

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

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

Cancel the common factor.

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

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

Rewrite the expression.

$15 x - 2 \cdot 2 - 10 x = - 5$

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

$15 x - 2 \cdot 2 - 10 x = - 5$

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

Multiply $- 2$ by $2$ .

$15 x - 4 - 10 x = - 5$

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

$15 x - 4 - 10 x = - 5$

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

Subtract $10 x$ from $15 x$ .

$5 x - 4 = - 5$

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

$5 x - 4 = - 5$

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

$5 x - 4 = - 5$

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

$5 x - 4 = - 5$

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

Step 3

Solve for $x$ in $5 x - 4 = - 5$ .

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

Add $4$ to both sides of the equation.

$5 x = - 5 + 4$

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

Add $- 5$ and $4$ .

$5 x = - 1$

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

$5 x = - 1$

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

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

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

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

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

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

Divide $x$ by $1$ .

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

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

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

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

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

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

Simplify the right side.

Move the negative in front of the fraction.

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

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

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

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

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

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

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

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

Step 4

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

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

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

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

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

Simplify the left side.

Remove parentheses.

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

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

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

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

Simplify the right side.

Simplify $\frac{2}{5} - \frac{1}{5}$ .

Combine the numerators over the common denominator.

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

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

Subtract $1$ from $2$ .

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

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

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

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

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

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

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

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

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

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

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=-5 , 5y=2+5x

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