Solve by Substitution x-y=0 , x+y=2

$x - y = 0$ , $x + y = 2$

Step 1

Add $y$ to both sides of the equation.

$x = y$

$x + y = 2$

Step 2

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

Replace all occurrences of $x$ in $x + y = 2$ with $y$ .

$(y) + y = 2$

$x = y$

Simplify the left side.

Add $y$ and $y$ .

$2 y = 2$

$x = y$

$2 y = 2$

$x = y$

$2 y = 2$

$x = y$

Step 3

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

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

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

$x = y$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

$x = y$

Divide $y$ by $1$ .

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

$x = y$

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

$x = y$

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

$x = y$

Simplify the right side.

Divide $2$ by $2$ .

$y = 1$

$x = y$

$y = 1$

$x = y$

$y = 1$

$x = y$

Step 4

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

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

$x = 1$

$y = 1$

Simplify the left side.

Remove parentheses.

$x = 1$

$y = 1$

$x = 1$

$y = 1$

$x = 1$

$y = 1$

Step 5

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

$(1, 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(1, 1)$

Equation Form:

$x = 1, y = 1$

Step 7

Solve by Substitution x-y=0 , x+y=2

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