Solve by Substitution x+y=1 , y-x=1

$x + y = 1$ , $y - x = 1$

Step 1

Subtract $y$ from both sides of the equation.

$x = 1 - y$

$y - x = 1$

Step 2

Replace all occurrences of $x$ with $1 - y$ in each equation.

Replace all occurrences of $x$ in $y - x = 1$ with $1 - y$ .

$y - (1 - y) = 1$

$x = 1 - y$

Simplify the left side.

Simplify $y - (1 - y)$ .

Simplify each term.

Apply the distributive property.

$y - 1 \cdot 1 + y = 1$

$x = 1 - y$

Multiply $- 1$ by $1$ .

$y - 1 + y = 1$

$x = 1 - y$

Multiply $- - y$ .

Multiply $- 1$ by $- 1$ .

$y - 1 + 1 y = 1$

$x = 1 - y$

Multiply $y$ by $1$ .

$y - 1 + y = 1$

$x = 1 - y$

$y - 1 + y = 1$

$x = 1 - y$

$y - 1 + y = 1$

$x = 1 - y$

Add $y$ and $y$ .

$2 y - 1 = 1$

$x = 1 - y$

$2 y - 1 = 1$

$x = 1 - y$

$2 y - 1 = 1$

$x = 1 - y$

$2 y - 1 = 1$

$x = 1 - y$

Step 3

Solve for $y$ in $2 y - 1 = 1$ .

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

Add $1$ to both sides of the equation.

$2 y = 1 + 1$

$x = 1 - y$

Add $1$ and $1$ .

$2 y = 2$

$x = 1 - y$

$2 y = 2$

$x = 1 - y$

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

Divide each term in $2 y = 2$ by $2$ .

$\frac{2 y}{2} = \frac{2}{2}$

$x = 1 - y$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{2}{2}$

$x = 1 - y$

Divide $y$ by $1$ .

$y = \frac{2}{2}$

$x = 1 - y$

$y = \frac{2}{2}$

$x = 1 - y$

$y = \frac{2}{2}$

$x = 1 - y$

Simplify the right side.

Divide $2$ by $2$ .

$y = 1$

$x = 1 - y$

$y = 1$

$x = 1 - y$

$y = 1$

$x = 1 - y$

$y = 1$

$x = 1 - y$

Step 4

Replace all occurrences of $y$ with $1$ in each equation.

Replace all occurrences of $y$ in $x = 1 - y$ with $1$ .

$x = 1 - (1)$

$y = 1$

Simplify the right side.

Simplify $1 - (1)$ .

Multiply $- 1$ by $1$ .

$x = 1 - 1$

$y = 1$

Subtract $1$ from $1$ .

$x = 0$

$y = 1$

$x = 0$

$y = 1$

$x = 0$

$y = 1$

$x = 0$

$y = 1$

Step 5

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

$(0, 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(0, 1)$

Equation Form:

$x = 0, y = 1$

Step 7

Solve by Substitution x+y=1 , y-x=1

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