Solve the System of Equations -x+y=1 -2x-y=-4

$- x + y = 1$ $- 2 x - y = - 4$

Step 1

Add $x$ to both sides of the equation.

$y = 1 + x$

$- 2 x - y = - 4$

Step 2

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

Replace all occurrences of $y$ in $- 2 x - y = - 4$ with $1 + x$ .

$- 2 x - (1 + x) = - 4$

$y = 1 + x$

Simplify the left side.

Simplify $- 2 x - (1 + x)$ .

Simplify each term.

Apply the distributive property.

$- 2 x - 1 \cdot 1 - x = - 4$

$y = 1 + x$

Multiply $- 1$ by $1$ .

$- 2 x - 1 - x = - 4$

$y = 1 + x$

$- 2 x - 1 - x = - 4$

$y = 1 + x$

Subtract $x$ from $- 2 x$ .

$- 3 x - 1 = - 4$

$y = 1 + x$

$- 3 x - 1 = - 4$

$y = 1 + x$

$- 3 x - 1 = - 4$

$y = 1 + x$

$- 3 x - 1 = - 4$

$y = 1 + x$

Step 3

Solve for $x$ in $- 3 x - 1 = - 4$ .

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

Add $1$ to both sides of the equation.

$- 3 x = - 4 + 1$

$y = 1 + x$

Add $- 4$ and $1$ .

$- 3 x = - 3$

$y = 1 + x$

$- 3 x = - 3$

$y = 1 + x$

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

Divide each term in $- 3 x = - 3$ by $- 3$ .

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

$y = 1 + x$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

$y = 1 + x$

Divide $x$ by $1$ .

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

$y = 1 + x$

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

$y = 1 + x$

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

$y = 1 + x$

Simplify the right side.

Divide $- 3$ by $- 3$ .

$x = 1$

$y = 1 + x$

$x = 1$

$y = 1 + x$

$x = 1$

$y = 1 + x$

$x = 1$

$y = 1 + x$

Step 4

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

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

$y = 1 + 1$

$x = 1$

Simplify $y = 1 + 1$ .

Simplify the left side.

Remove parentheses.

$y = 1 + 1$

$x = 1$

$y = 1 + 1$

$x = 1$

Simplify the right side.

Add $1$ and $1$ .

$y = 2$

$x = 1$

$y = 2$

$x = 1$

$y = 2$

$x = 1$

$y = 2$

$x = 1$

Step 5

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

$(1, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(1, 2)$

Equation Form:

$x = 1, y = 2$

Step 7

Solve the System of Equations -x+y=1 -2x-y=-4

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