Solve the System of Equations -x+y=-8 -4x+y=-33

$- x + y = - 8$ $- 4 x + y = - 33$

Step 1

Add $x$ to both sides of the equation.

$y = - 8 + x$

$- 4 x + y = - 33$

Step 2

Replace all occurrences of $y$ with $- 8 + x$ in each equation.

Replace all occurrences of $y$ in $- 4 x + y = - 33$ with $- 8 + x$ .

$- 4 x - 8 + x = - 33$

$y = - 8 + x$

Simplify the left side.

Simplify $- 4 x - 8 + x$ .

Remove parentheses.

$- 4 x - 8 + x = - 33$

$y = - 8 + x$

Add $- 4 x$ and $x$ .

$- 3 x - 8 = - 33$

$y = - 8 + x$

$- 3 x - 8 = - 33$

$y = - 8 + x$

$- 3 x - 8 = - 33$

$y = - 8 + x$

$- 3 x - 8 = - 33$

$y = - 8 + x$

Step 3

Solve for $x$ in $- 3 x - 8 = - 33$ .

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

Add $8$ to both sides of the equation.

$- 3 x = - 33 + 8$

$y = - 8 + x$

Add $- 33$ and $8$ .

$- 3 x = - 25$

$y = - 8 + x$

$- 3 x = - 25$

$y = - 8 + x$

Divide each term in $- 3 x = - 25$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 25$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 25}{- 3}$

$y = - 8 + x$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 25}{- 3}$

$y = - 8 + x$

Divide $x$ by $1$ .

$x = \frac{- 25}{- 3}$

$y = - 8 + x$

$x = \frac{- 25}{- 3}$

$y = - 8 + x$

$x = \frac{- 25}{- 3}$

$y = - 8 + x$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{25}{3}$

$y = - 8 + x$

$x = \frac{25}{3}$

$y = - 8 + x$

$x = \frac{25}{3}$

$y = - 8 + x$

$x = \frac{25}{3}$

$y = - 8 + x$

Step 4

Replace all occurrences of $x$ with $\frac{25}{3}$ in each equation.

Replace all occurrences of $x$ in $y = - 8 + x$ with $\frac{25}{3}$ .

$y = - 8 + \frac{25}{3}$

$x = \frac{25}{3}$

Simplify $y = - 8 + \frac{25}{3}$ .

Simplify the left side.

Remove parentheses.

$y = - 8 + \frac{25}{3}$

$x = \frac{25}{3}$

$y = - 8 + \frac{25}{3}$

$x = \frac{25}{3}$

Simplify the right side.

Simplify $- 8 + \frac{25}{3}$ .

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = - 8 \cdot \frac{3}{3} + \frac{25}{3}$

$x = \frac{25}{3}$

Combine $- 8$ and $\frac{3}{3}$ .

$y = \frac{- 8 \cdot 3}{3} + \frac{25}{3}$

$x = \frac{25}{3}$

Combine the numerators over the common denominator.

$y = \frac{- 8 \cdot 3 + 25}{3}$

$x = \frac{25}{3}$

Simplify the numerator.

Multiply $- 8$ by $3$ .

$y = \frac{- 24 + 25}{3}$

$x = \frac{25}{3}$

Add $- 24$ and $25$ .

$y = \frac{1}{3}$

$x = \frac{25}{3}$

$y = \frac{1}{3}$

$x = \frac{25}{3}$

$y = \frac{1}{3}$

$x = \frac{25}{3}$

$y = \frac{1}{3}$

$x = \frac{25}{3}$

$y = \frac{1}{3}$

$x = \frac{25}{3}$

$y = \frac{1}{3}$

$x = \frac{25}{3}$

Step 5

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

$(\frac{25}{3}, \frac{1}{3})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(\frac{25}{3}, \frac{1}{3})$

Equation Form:

$x = \frac{25}{3}, y = \frac{1}{3}$

Step 7

Solve the System of Equations -x+y=-8 -4x+y=-33

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