Solve the System of Equations x+y=5 x-y=1

$x + y = 5$ $x - y = 1$

Step 1

Subtract $y$ from both sides of the equation.

$x = 5 - y$

$x - y = 1$

Step 2

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

Replace all occurrences of $x$ in $x - y = 1$ with $5 - y$ .

$(5 - y) - y = 1$

$x = 5 - y$

Simplify the left side.

Subtract $y$ from $- y$ .

$5 - 2 y = 1$

$x = 5 - y$

$5 - 2 y = 1$

$x = 5 - y$

$5 - 2 y = 1$

$x = 5 - y$

Step 3

Solve for $y$ in $5 - 2 y = 1$ .

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

Subtract $5$ from both sides of the equation.

$- 2 y = 1 - 5$

$x = 5 - y$

Subtract $5$ from $1$ .

$- 2 y = - 4$

$x = 5 - y$

$- 2 y = - 4$

$x = 5 - y$

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

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

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

$x = 5 - y$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

$x = 5 - y$

Divide $y$ by $1$ .

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

$x = 5 - y$

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

$x = 5 - y$

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

$x = 5 - y$

Simplify the right side.

Divide $- 4$ by $- 2$ .

$y = 2$

$x = 5 - y$

$y = 2$

$x = 5 - y$

$y = 2$

$x = 5 - y$

$y = 2$

$x = 5 - y$

Step 4

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

Replace all occurrences of $y$ in $x = 5 - y$ with $2$ .

$x = 5 - (2)$

$y = 2$

Simplify the right side.

Simplify $5 - (2)$ .

Multiply $- 1$ by $2$ .

$x = 5 - 2$

$y = 2$

Subtract $2$ from $5$ .

$x = 3$

$y = 2$

$x = 3$

$y = 2$

$x = 3$

$y = 2$

$x = 3$

$y = 2$

Step 5

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

$(3, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(3, 2)$

Equation Form:

$x = 3, y = 2$

Step 7

Solve the System of Equations x+y=5 x-y=1

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