Solve by Substitution x+5y=5 , -x-5y=5

$x + 5 y = 5$ , $- x - 5 y = 5$

Step 1

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

$x = 5 - 5 y$

$- x - 5 y = 5$

Step 2

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

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

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

$x = 5 - 5 y$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

$- 1 \cdot 5 - (- 5 y) - 5 y = 5$

$x = 5 - 5 y$

Multiply $- 1$ by $5$ .

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

$x = 5 - 5 y$

Multiply $- 5$ by $- 1$ .

$- 5 + 5 y - 5 y = 5$

$x = 5 - 5 y$

$- 5 + 5 y - 5 y = 5$

$x = 5 - 5 y$

Combine the opposite terms in $- 5 + 5 y - 5 y$ .

Subtract $5 y$ from $5 y$ .

$- 5 + 0 = 5$

$x = 5 - 5 y$

Add $- 5$ and $0$ .

$- 5 = 5$

$x = 5 - 5 y$

$- 5 = 5$

$x = 5 - 5 y$

$- 5 = 5$

$x = 5 - 5 y$

$- 5 = 5$

$x = 5 - 5 y$

$- 5 = 5$

$x = 5 - 5 y$

Step 3

Since $- 5 = 5$ is not true, there is no solution.

No solution

Step 4