Solve the System of Equations -x+y=1 x+y=11

$- x + y = 1$ $x + y = 11$

Step 1

Add $x$ to both sides of the equation.

$y = 1 + x$

$x + y = 11$

Step 2

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

Replace all occurrences of $y$ in $x + y = 11$ with $1 + x$ .

$x + 1 + x = 11$

$y = 1 + x$

Simplify the left side.

Simplify $x + 1 + x$ .

Remove parentheses.

$x + 1 + x = 11$

$y = 1 + x$

Add $x$ and $x$ .

$2 x + 1 = 11$

$y = 1 + x$

$2 x + 1 = 11$

$y = 1 + x$

$2 x + 1 = 11$

$y = 1 + x$

$2 x + 1 = 11$

$y = 1 + x$

Step 3

Solve for $x$ in $2 x + 1 = 11$ .

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

Subtract $1$ from both sides of the equation.

$2 x = 11 - 1$

$y = 1 + x$

Subtract $1$ from $11$ .

$2 x = 10$

$y = 1 + x$

$2 x = 10$

$y = 1 + x$

Divide each term in $2 x = 10$ by $2$ and simplify.

Divide each term in $2 x = 10$ by $2$ .

$\frac{2 x}{2} = \frac{10}{2}$

$y = 1 + x$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{10}{2}$

$y = 1 + x$

Divide $x$ by $1$ .

$x = \frac{10}{2}$

$y = 1 + x$

$x = \frac{10}{2}$

$y = 1 + x$

$x = \frac{10}{2}$

$y = 1 + x$

Simplify the right side.

Divide $10$ by $2$ .

$x = 5$

$y = 1 + x$

$x = 5$

$y = 1 + x$

$x = 5$

$y = 1 + x$

$x = 5$

$y = 1 + x$

Step 4

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

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

$y = 1 + 5$

$x = 5$

Simplify $y = 1 + 5$ .

Simplify the left side.

Remove parentheses.

$y = 1 + 5$

$x = 5$

$y = 1 + 5$

$x = 5$

Simplify the right side.

Add $1$ and $5$ .

$y = 6$

$x = 5$

$y = 6$

$x = 5$

$y = 6$

$x = 5$

$y = 6$

$x = 5$

Step 5

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

$(5, 6)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(5, 6)$

Equation Form:

$x = 5, y = 6$

Step 7

Solve the System of Equations -x+y=1 x+y=11

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