Solve by Substitution x+y=1 , x-y=-2

$x + y = 1$ , $x - y = - 2$

Step 1

Subtract $y$ from both sides of the equation.

$x = 1 - y$

$x - y = - 2$

Step 2

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

Replace all occurrences of $x$ in $x - y = - 2$ with $1 - y$ .

$(1 - y) - y = - 2$

$x = 1 - y$

Simplify the left side.

Subtract $y$ from $- y$ .

$1 - 2 y = - 2$

$x = 1 - y$

$1 - 2 y = - 2$

$x = 1 - y$

$1 - 2 y = - 2$

$x = 1 - y$

Step 3

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

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

Subtract $1$ from both sides of the equation.

$- 2 y = - 2 - 1$

$x = 1 - y$

Subtract $1$ from $- 2$ .

$- 2 y = - 3$

$x = 1 - y$

$- 2 y = - 3$

$x = 1 - y$

Divide each term in $- 2 y = - 3$ by $- 2$ and simplify.

Divide each term in $- 2 y = - 3$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 3}{- 2}$

$x = 1 - y$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 3}{- 2}$

$x = 1 - y$

Divide $y$ by $1$ .

$y = \frac{- 3}{- 2}$

$x = 1 - y$

$y = \frac{- 3}{- 2}$

$x = 1 - y$

$y = \frac{- 3}{- 2}$

$x = 1 - y$

Simplify the right side.

Dividing two negative values results in a positive value.

$y = \frac{3}{2}$

$x = 1 - y$

$y = \frac{3}{2}$

$x = 1 - y$

$y = \frac{3}{2}$

$x = 1 - y$

$y = \frac{3}{2}$

$x = 1 - y$

Step 4

Replace all occurrences of $y$ with $\frac{3}{2}$ in each equation.

Replace all occurrences of $y$ in $x = 1 - y$ with $\frac{3}{2}$ .

$x = 1 - (\frac{3}{2})$

$y = \frac{3}{2}$

Simplify the right side.

Simplify $1 - (\frac{3}{2})$ .

Write $1$ as a fraction with a common denominator.

$x = \frac{2}{2} - \frac{3}{2}$

$y = \frac{3}{2}$

Combine the numerators over the common denominator.

$x = \frac{2 - 3}{2}$

$y = \frac{3}{2}$

Subtract $3$ from $2$ .

$x = \frac{- 1}{2}$

$y = \frac{3}{2}$

Move the negative in front of the fraction.

$x = - \frac{1}{2}$

$y = \frac{3}{2}$

$x = - \frac{1}{2}$

$y = \frac{3}{2}$

$x = - \frac{1}{2}$

$y = \frac{3}{2}$

$x = - \frac{1}{2}$

$y = \frac{3}{2}$

Step 5

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

$(- \frac{1}{2}, \frac{3}{2})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- \frac{1}{2}, \frac{3}{2})$

Equation Form:

$x = - \frac{1}{2}, y = \frac{3}{2}$

Step 7

Solve by Substitution x+y=1 , x-y=-2

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