Solve the System of Equations x+5y=5 3x-5y=3

$x + 5 y = 5$ $3 x - 5 y = 3$

Step 1

Subtract $5 y$ from both sides of the equation.

$x = 5 - 5 y$

$3 x - 5 y = 3$

Step 2

Replace all occurrences of $x$ with $5 - 5 y$ in each equation.

Replace all occurrences of $x$ in $3 x - 5 y = 3$ with $5 - 5 y$ .

$3 (5 - 5 y) - 5 y = 3$

$x = 5 - 5 y$

Simplify the left side.

Simplify $3 (5 - 5 y) - 5 y$ .

Simplify each term.

Apply the distributive property.

$3 \cdot 5 + 3 (- 5 y) - 5 y = 3$

$x = 5 - 5 y$

Multiply $3$ by $5$ .

$15 + 3 (- 5 y) - 5 y = 3$

$x = 5 - 5 y$

Multiply $- 5$ by $3$ .

$15 - 15 y - 5 y = 3$

$x = 5 - 5 y$

$15 - 15 y - 5 y = 3$

$x = 5 - 5 y$

Subtract $5 y$ from $- 15 y$ .

$15 - 20 y = 3$

$x = 5 - 5 y$

$15 - 20 y = 3$

$x = 5 - 5 y$

$15 - 20 y = 3$

$x = 5 - 5 y$

$15 - 20 y = 3$

$x = 5 - 5 y$

Step 3

Solve for $y$ in $15 - 20 y = 3$ .

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

Subtract $15$ from both sides of the equation.

$- 20 y = 3 - 15$

$x = 5 - 5 y$

Subtract $15$ from $3$ .

$- 20 y = - 12$

$x = 5 - 5 y$

$- 20 y = - 12$

$x = 5 - 5 y$

Divide each term in $- 20 y = - 12$ by $- 20$ and simplify.

Divide each term in $- 20 y = - 12$ by $- 20$ .

$\frac{- 20 y}{- 20} = \frac{- 12}{- 20}$

$x = 5 - 5 y$

Simplify the left side.

Cancel the common factor of $- 20$ .

Cancel the common factor.

$\frac{- 20 y}{- 20} = \frac{- 12}{- 20}$

$x = 5 - 5 y$

Divide $y$ by $1$ .

$y = \frac{- 12}{- 20}$

$x = 5 - 5 y$

$y = \frac{- 12}{- 20}$

$x = 5 - 5 y$

$y = \frac{- 12}{- 20}$

$x = 5 - 5 y$

Simplify the right side.

Cancel the common factor of $- 12$ and $- 20$ .

Factor $- 4$ out of $- 12$ .

$y = \frac{- 4 \cdot 3}{- 20}$

$x = 5 - 5 y$

Cancel the common factors.

Factor $- 4$ out of $- 20$ .

$y = \frac{- 4 \cdot 3}{- 4 \cdot 5}$

$x = 5 - 5 y$

Cancel the common factor.

$y = \frac{- 4 \cdot 3}{- 4 \cdot 5}$

$x = 5 - 5 y$

Rewrite the expression.

$y = \frac{3}{5}$

$x = 5 - 5 y$

$y = \frac{3}{5}$

$x = 5 - 5 y$

$y = \frac{3}{5}$

$x = 5 - 5 y$

$y = \frac{3}{5}$

$x = 5 - 5 y$

$y = \frac{3}{5}$

$x = 5 - 5 y$

$y = \frac{3}{5}$

$x = 5 - 5 y$

Step 4

Replace all occurrences of $y$ with $\frac{3}{5}$ in each equation.

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

$x = 5 - 5 (\frac{3}{5})$

$y = \frac{3}{5}$

Simplify the right side.

Simplify $5 - 5 (\frac{3}{5})$ .

Simplify each term.

Cancel the common factor of $5$ .

Factor $5$ out of $- 5$ .

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

$y = \frac{3}{5}$

Cancel the common factor.

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

$y = \frac{3}{5}$

Rewrite the expression.

$x = 5 - 1 \cdot 3$

$y = \frac{3}{5}$

$x = 5 - 1 \cdot 3$

$y = \frac{3}{5}$

Multiply $- 1$ by $3$ .

$x = 5 - 3$

$y = \frac{3}{5}$

$x = 5 - 3$

$y = \frac{3}{5}$

Subtract $3$ from $5$ .

$x = 2$

$y = \frac{3}{5}$

$x = 2$

$y = \frac{3}{5}$

$x = 2$

$y = \frac{3}{5}$

$x = 2$

$y = \frac{3}{5}$

Step 5

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

$(2, \frac{3}{5})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(2, \frac{3}{5})$

Equation Form:

$x = 2, y = \frac{3}{5}$

Step 7

Solve the System of Equations x+5y=5 3x-5y=3

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