Solve by Substitution x-y=2 , x+y=6

$x - y = 2$ , $x + y = 6$

Step 1

Add $y$ to both sides of the equation.

$x = 2 + y$

$x + y = 6$

Step 2

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

Replace all occurrences of $x$ in $x + y = 6$ with $2 + y$ .

$(2 + y) + y = 6$

$x = 2 + y$

Simplify the left side.

Add $y$ and $y$ .

$2 + 2 y = 6$

$x = 2 + y$

$2 + 2 y = 6$

$x = 2 + y$

$2 + 2 y = 6$

$x = 2 + y$

Step 3

Solve for $y$ in $2 + 2 y = 6$ .

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

Subtract $2$ from both sides of the equation.

$2 y = 6 - 2$

$x = 2 + y$

Subtract $2$ from $6$ .

$2 y = 4$

$x = 2 + y$

$2 y = 4$

$x = 2 + y$

Divide each term in $2 y = 4$ by $2$ and simplify.

Divide each term in $2 y = 4$ by $2$ .

$\frac{2 y}{2} = \frac{4}{2}$

$x = 2 + y$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{4}{2}$

$x = 2 + y$

Divide $y$ by $1$ .

$y = \frac{4}{2}$

$x = 2 + y$

$y = \frac{4}{2}$

$x = 2 + y$

$y = \frac{4}{2}$

$x = 2 + y$

Simplify the right side.

Divide $4$ by $2$ .

$y = 2$

$x = 2 + y$

$y = 2$

$x = 2 + y$

$y = 2$

$x = 2 + y$

$y = 2$

$x = 2 + y$

Step 4

Replace all occurrences of $y$ with $2$ in each equation.

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

$x = 2 + 2$

$y = 2$

Simplify $x = 2 + 2$ .

Simplify the left side.

Remove parentheses.

$x = 2 + 2$

$y = 2$

$x = 2 + 2$

$y = 2$

Simplify the right side.

Add $2$ and $2$ .

$x = 4$

$y = 2$

$x = 4$

$y = 2$

$x = 4$

$y = 2$

$x = 4$

$y = 2$

Step 5

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

$(4, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, 2)$

Equation Form:

$x = 4, y = 2$

Step 7

Solve by Substitution x-y=2 , x+y=6

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