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.

Simplify each term.

Move the negative in front of the fraction.

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

$15 x - 10 y = 5$

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 $1$ .

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

$15 x - 10 y = 5$

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

$15 x - 10 y = 5$

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

$15 x - 10 y = 5$

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

$15 x - 10 y = 5$

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

$15 x - 10 y = 5$

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 $5$ .

Move the leading negative in $- \frac{2}{5}$ into the numerator.

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

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

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.

Subtract $4$ from both sides of the equation.

$5 x = 5 - 4$

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

Subtract $4$ from $5$ .

$5 x = 1$

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

$5 x = 1$

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

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 $1$ .

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

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

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

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

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

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

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

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

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

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

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.

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

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

Simplify the expression.

Add $- 2$ and $1$ .

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

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

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=5 , 5y=-2+5x

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