Solve by Substitution -x-7y=14 , -4x-14y=28

$- x - 7 y = 14$ , $- 4 x - 14 y = 28$

Step 1

Solve for $x$ in $- x - 7 y = 14$ .

Add $7 y$ to both sides of the equation.

$- x = 14 + 7 y$

$- 4 x - 14 y = 28$

Divide each term in $- x = 14 + 7 y$ by $- 1$ and simplify.

Divide each term in $- x = 14 + 7 y$ by $- 1$ .

$\frac{- x}{- 1} = \frac{14}{- 1} + \frac{7 y}{- 1}$

$- 4 x - 14 y = 28$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{14}{- 1} + \frac{7 y}{- 1}$

$- 4 x - 14 y = 28$

Divide $x$ by $1$ .

$x = \frac{14}{- 1} + \frac{7 y}{- 1}$

$- 4 x - 14 y = 28$

$x = \frac{14}{- 1} + \frac{7 y}{- 1}$

$- 4 x - 14 y = 28$

Simplify the right side.

Simplify each term.

Divide $14$ by $- 1$ .

$x = - 14 + \frac{7 y}{- 1}$

$- 4 x - 14 y = 28$

Move the negative one from the denominator of $\frac{7 y}{- 1}$ .

$x = - 14 - 1 \cdot (7 y)$

$- 4 x - 14 y = 28$

Rewrite $- 1 \cdot (7 y)$ as $- (7 y)$ .

$x = - 14 - (7 y)$

$- 4 x - 14 y = 28$

Multiply $7$ by $- 1$ .

$x = - 14 - 7 y$

$- 4 x - 14 y = 28$

$x = - 14 - 7 y$

$- 4 x - 14 y = 28$

$x = - 14 - 7 y$

$- 4 x - 14 y = 28$

$x = - 14 - 7 y$

$- 4 x - 14 y = 28$

$x = - 14 - 7 y$

$- 4 x - 14 y = 28$

Step 2

Replace all occurrences of $x$ with $- 14 - 7 y$ in each equation.

Replace all occurrences of $x$ in $- 4 x - 14 y = 28$ with $- 14 - 7 y$ .

$- 4 (- 14 - 7 y) - 14 y = 28$

$x = - 14 - 7 y$

Simplify the left side.

Simplify $- 4 (- 14 - 7 y) - 14 y$ .

Simplify each term.

Apply the distributive property.

$- 4 \cdot - 14 - 4 (- 7 y) - 14 y = 28$

$x = - 14 - 7 y$

Multiply $- 4$ by $- 14$ .

$56 - 4 (- 7 y) - 14 y = 28$

$x = - 14 - 7 y$

Multiply $- 7$ by $- 4$ .

$56 + 28 y - 14 y = 28$

$x = - 14 - 7 y$

$56 + 28 y - 14 y = 28$

$x = - 14 - 7 y$

Subtract $14 y$ from $28 y$ .

$56 + 14 y = 28$

$x = - 14 - 7 y$

$56 + 14 y = 28$

$x = - 14 - 7 y$

$56 + 14 y = 28$

$x = - 14 - 7 y$

$56 + 14 y = 28$

$x = - 14 - 7 y$

Step 3

Solve for $y$ in $56 + 14 y = 28$ .

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

Subtract $56$ from both sides of the equation.

$14 y = 28 - 56$

$x = - 14 - 7 y$

Subtract $56$ from $28$ .

$14 y = - 28$

$x = - 14 - 7 y$

$14 y = - 28$

$x = - 14 - 7 y$

Divide each term in $14 y = - 28$ by $14$ and simplify.

Divide each term in $14 y = - 28$ by $14$ .

$\frac{14 y}{14} = \frac{- 28}{14}$

$x = - 14 - 7 y$

Simplify the left side.

Cancel the common factor of $14$ .

Cancel the common factor.

$\frac{14 y}{14} = \frac{- 28}{14}$

$x = - 14 - 7 y$

Divide $y$ by $1$ .

$y = \frac{- 28}{14}$

$x = - 14 - 7 y$

$y = \frac{- 28}{14}$

$x = - 14 - 7 y$

$y = \frac{- 28}{14}$

$x = - 14 - 7 y$

Simplify the right side.

Divide $- 28$ by $14$ .

$y = - 2$

$x = - 14 - 7 y$

$y = - 2$

$x = - 14 - 7 y$

$y = - 2$

$x = - 14 - 7 y$

$y = - 2$

$x = - 14 - 7 y$

Step 4

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

Replace all occurrences of $y$ in $x = - 14 - 7 y$ with $- 2$ .

$x = - 14 - 7 \cdot - 2$

$y = - 2$

Simplify the right side.

Simplify $- 14 - 7 \cdot - 2$ .

Multiply $- 7$ by $- 2$ .

$x = - 14 + 14$

$y = - 2$

Add $- 14$ and $14$ .

$x = 0$

$y = - 2$

$x = 0$

$y = - 2$

$x = 0$

$y = - 2$

$x = 0$

$y = - 2$

Step 5

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

$(0, - 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(0, - 2)$

Equation Form:

$x = 0, y = - 2$

Step 7

Solve by Substitution -x-7y=14 , -4x-14y=28

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