Solve the System of Equations -x+3y=-6 and 4x+7y=-33

$- x + 3 y = - 6$ and $4 x + 7 y = - 33$

Solve for $x$ in $- x + 3 y = - 6$ .

Subtract $3 y$ from both sides of the equation.

$- x = - 6 - 3 y$

$4 x + 7 y = - 33$

Divide each term in $- x = - 6 - 3 y$ by $- 1$ and simplify.

Divide each term in $- x = - 6 - 3 y$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 6}{- 1} + \frac{- 3 y}{- 1}$

$4 x + 7 y = - 33$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 6}{- 1} + \frac{- 3 y}{- 1}$

$4 x + 7 y = - 33$

Divide $x$ by $1$ .

$x = \frac{- 6}{- 1} + \frac{- 3 y}{- 1}$

$4 x + 7 y = - 33$

$x = \frac{- 6}{- 1} + \frac{- 3 y}{- 1}$

$4 x + 7 y = - 33$

Simplify the right side.

Simplify each term.

Divide $- 6$ by $- 1$ .

$x = 6 + \frac{- 3 y}{- 1}$

$4 x + 7 y = - 33$

Move the negative one from the denominator of $\frac{- 3 y}{- 1}$ .

$x = 6 - 1 \cdot (- 3 y)$

$4 x + 7 y = - 33$

Rewrite $- 1 \cdot (- 3 y)$ as $- (- 3 y)$ .

$x = 6 - (- 3 y)$

$4 x + 7 y = - 33$

Multiply $- 3$ by $- 1$ .

$x = 6 + 3 y$

$4 x + 7 y = - 33$

$x = 6 + 3 y$

$4 x + 7 y = - 33$

$x = 6 + 3 y$

$4 x + 7 y = - 33$

$x = 6 + 3 y$

$4 x + 7 y = - 33$

$x = 6 + 3 y$

$4 x + 7 y = - 33$

Replace all occurrences of $x$ with $6 + 3 y$ in each equation.

Replace all occurrences of $x$ in $4 x + 7 y = - 33$ with $6 + 3 y$ .

$4 (6 + 3 y) + 7 y = - 33$

$x = 6 + 3 y$

Simplify the left side.

Simplify $4 (6 + 3 y) + 7 y$ .

Simplify each term.

Apply the distributive property.

$4 \cdot 6 + 4 (3 y) + 7 y = - 33$

$x = 6 + 3 y$

Multiply $4$ by $6$ .

$24 + 4 (3 y) + 7 y = - 33$

$x = 6 + 3 y$

Multiply $3$ by $4$ .

$24 + 12 y + 7 y = - 33$

$x = 6 + 3 y$

$24 + 12 y + 7 y = - 33$

$x = 6 + 3 y$

Add $12 y$ and $7 y$ .

$24 + 19 y = - 33$

$x = 6 + 3 y$

$24 + 19 y = - 33$

$x = 6 + 3 y$

$24 + 19 y = - 33$

$x = 6 + 3 y$

$24 + 19 y = - 33$

$x = 6 + 3 y$

Solve for $y$ in $24 + 19 y = - 33$ .

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

Subtract $24$ from both sides of the equation.

$19 y = - 33 - 24$

$x = 6 + 3 y$

Subtract $24$ from $- 33$ .

$19 y = - 57$

$x = 6 + 3 y$

$19 y = - 57$

$x = 6 + 3 y$

Divide each term in $19 y = - 57$ by $19$ and simplify.

Divide each term in $19 y = - 57$ by $19$ .

$\frac{19 y}{19} = \frac{- 57}{19}$

$x = 6 + 3 y$

Simplify the left side.

Cancel the common factor of $19$ .

Cancel the common factor.

$\frac{19 y}{19} = \frac{- 57}{19}$

$x = 6 + 3 y$

Divide $y$ by $1$ .

$y = \frac{- 57}{19}$

$x = 6 + 3 y$

$y = \frac{- 57}{19}$

$x = 6 + 3 y$

$y = \frac{- 57}{19}$

$x = 6 + 3 y$

Simplify the right side.

Divide $- 57$ by $19$ .

$y = - 3$

$x = 6 + 3 y$

$y = - 3$

$x = 6 + 3 y$

$y = - 3$

$x = 6 + 3 y$

$y = - 3$

$x = 6 + 3 y$

Replace all occurrences of $y$ with $- 3$ in each equation.

Replace all occurrences of $y$ in $x = 6 + 3 y$ with $- 3$ .

$x = 6 + 3 (- 3)$

$y = - 3$

Simplify the right side.

Simplify $6 + 3 (- 3)$ .

Multiply $3$ by $- 3$ .

$x = 6 - 9$

$y = - 3$

Subtract $9$ from $6$ .

$x = - 3$

$y = - 3$

$x = - 3$

$y = - 3$

$x = - 3$

$y = - 3$

$x = - 3$

$y = - 3$

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

$(- 3, - 3)$

The result can be shown in multiple forms.

Point Form:

$(- 3, - 3)$

Equation Form:

$x = - 3, y = - 3$

Solve the System of Equations -x+3y=-6 and 4x+7y=-33

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