Solve the System of Equations -x+y=1 x-y=1

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

Add $x$ to both sides of the equation.

$y = 1 + x$

$x - y = 1$

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

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

$x - (1 + x) = 1$

$y = 1 + x$

Simplify the left side.

Simplify $x - (1 + x)$ .

Simplify each term.

Apply the distributive property.

$x - 1 \cdot 1 - x = 1$

$y = 1 + x$

Multiply $- 1$ by $1$ .

$x - 1 - x = 1$

$y = 1 + x$

$x - 1 - x = 1$

$y = 1 + x$

Combine the opposite terms in $x - 1 - x$ .

Subtract $x$ from $x$ .

$0 - 1 = 1$

$y = 1 + x$

Subtract $1$ from $0$ .

$- 1 = 1$

$y = 1 + x$

$- 1 = 1$

$y = 1 + x$

$- 1 = 1$

$y = 1 + x$

$- 1 = 1$

$y = 1 + x$

$- 1 = 1$

$y = 1 + x$

Since $- 1 = 1$ is not true, there is no solution.

No solution

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