Solve the System of Equations x+y=7 x-y=1

$x + y = 7$ $x - y = 1$

Step 1

Subtract $y$ from both sides of the equation.

$x = 7 - y$

$x - y = 1$

Step 2

Replace all occurrences of $x$ with $7 - y$ in each equation.

Replace all occurrences of $x$ in $x - y = 1$ with $7 - y$ .

$(7 - y) - y = 1$

$x = 7 - y$

Simplify the left side.

Subtract $y$ from $- y$ .

$7 - 2 y = 1$

$x = 7 - y$

$7 - 2 y = 1$

$x = 7 - y$

$7 - 2 y = 1$

$x = 7 - y$

Step 3

Solve for $y$ in $7 - 2 y = 1$ .

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

Subtract $7$ from both sides of the equation.

$- 2 y = 1 - 7$

$x = 7 - y$

Subtract $7$ from $1$ .

$- 2 y = - 6$

$x = 7 - y$

$- 2 y = - 6$

$x = 7 - y$

Divide each term in $- 2 y = - 6$ by $- 2$ and simplify.

Divide each term in $- 2 y = - 6$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 6}{- 2}$

$x = 7 - y$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 6}{- 2}$

$x = 7 - y$

Divide $y$ by $1$ .

$y = \frac{- 6}{- 2}$

$x = 7 - y$

$y = \frac{- 6}{- 2}$

$x = 7 - y$

$y = \frac{- 6}{- 2}$

$x = 7 - y$

Simplify the right side.

Divide $- 6$ by $- 2$ .

$y = 3$

$x = 7 - y$

$y = 3$

$x = 7 - y$

$y = 3$

$x = 7 - y$

$y = 3$

$x = 7 - y$

Step 4

Replace all occurrences of $y$ with $3$ in each equation.

Replace all occurrences of $y$ in $x = 7 - y$ with $3$ .

$x = 7 - (3)$

$y = 3$

Simplify the right side.

Simplify $7 - (3)$ .

Multiply $- 1$ by $3$ .

$x = 7 - 3$

$y = 3$

Subtract $3$ from $7$ .

$x = 4$

$y = 3$

$x = 4$

$y = 3$

$x = 4$

$y = 3$

$x = 4$

$y = 3$

Step 5

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

$(4, 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, 3)$

Equation Form:

$x = 4, y = 3$

Step 7

Solve the System of Equations x+y=7 x-y=1

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