Solve the System of Equations -x+y=4 x+3y=4

$- x + y = 4$ $x + 3 y = 4$

Step 1

Add $x$ to both sides of the equation.

$y = 4 + x$

$x + 3 y = 4$

Step 2

Replace all occurrences of $y$ with $4 + x$ in each equation.

Replace all occurrences of $y$ in $x + 3 y = 4$ with $4 + x$ .

$x + 3 (4 + x) = 4$

$y = 4 + x$

Simplify the left side.

Simplify $x + 3 (4 + x)$ .

Simplify each term.

Apply the distributive property.

$x + 3 \cdot 4 + 3 x = 4$

$y = 4 + x$

Multiply $3$ by $4$ .

$x + 12 + 3 x = 4$

$y = 4 + x$

$x + 12 + 3 x = 4$

$y = 4 + x$

Add $x$ and $3 x$ .

$4 x + 12 = 4$

$y = 4 + x$

$4 x + 12 = 4$

$y = 4 + x$

$4 x + 12 = 4$

$y = 4 + x$

$4 x + 12 = 4$

$y = 4 + x$

Step 3

Solve for $x$ in $4 x + 12 = 4$ .

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

Subtract $12$ from both sides of the equation.

$4 x = 4 - 12$

$y = 4 + x$

Subtract $12$ from $4$ .

$4 x = - 8$

$y = 4 + x$

$4 x = - 8$

$y = 4 + x$

Divide each term in $4 x = - 8$ by $4$ and simplify.

Divide each term in $4 x = - 8$ by $4$ .

$\frac{4 x}{4} = \frac{- 8}{4}$

$y = 4 + x$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 8}{4}$

$y = 4 + x$

Divide $x$ by $1$ .

$x = \frac{- 8}{4}$

$y = 4 + x$

$x = \frac{- 8}{4}$

$y = 4 + x$

$x = \frac{- 8}{4}$

$y = 4 + x$

Simplify the right side.

Divide $- 8$ by $4$ .

$x = - 2$

$y = 4 + x$

$x = - 2$

$y = 4 + x$

$x = - 2$

$y = 4 + x$

$x = - 2$

$y = 4 + x$

Step 4

Replace all occurrences of $x$ with $- 2$ in each equation.

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

$y = 4 - 2$

$x = - 2$

Simplify $y = 4 - 2$ .

Simplify the left side.

Remove parentheses.

$y = 4 - 2$

$x = - 2$

$y = 4 - 2$

$x = - 2$

Simplify the right side.

Subtract $2$ from $4$ .

$y = 2$

$x = - 2$

$y = 2$

$x = - 2$

$y = 2$

$x = - 2$

$y = 2$

$x = - 2$

Step 5

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

$(- 2, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 2, 2)$

Equation Form:

$x = - 2, y = 2$

Step 7

Solve the System of Equations -x+y=4 x+3y=4

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