Determine if Linear 7x(y+2)=5-7y(6-x)

$7 x (y + 2) = 5 - 7 y (6 - x)$

Step 1

Solve the equation for $y$ .

Simplify $7 x (y + 2)$ .

Rewrite.

$0 + 0 + 7 x (y + 2) = 5 - 7 y (6 - x)$

Simplify by adding zeros.

$7 x (y + 2) = 5 - 7 y (6 - x)$

Apply the distributive property.

$7 x y + 7 x \cdot 2 = 5 - 7 y (6 - x)$

Multiply $2$ by $7$ .

$7 x y + 14 x = 5 - 7 y (6 - x)$

Simplify each term.

Apply the distributive property.

$7 x y + 14 x = 5 - 7 y \cdot 6 - 7 y (- x)$

Multiply $6$ by $- 7$ .

$7 x y + 14 x = 5 - 42 y - 7 y (- x)$

Rewrite using the commutative property of multiplication.

$7 x y + 14 x = 5 - 42 y - 7 \cdot - 1 y x$

Multiply $- 7$ by $- 1$ .

$7 x y + 14 x = 5 - 42 y + 7 y x$

Since $y$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$5 - 42 y + 7 y x = 7 x y + 14 x$

Move all terms containing $y$ to the left side of the equation.

Subtract $7 x y$ from both sides of the equation.

$5 - 42 y + 7 y x - 7 x y = 14 x$

Combine the opposite terms in $5 - 42 y + 7 y x - 7 x y$ .

Reorder the factors in the terms $7 y x$ and $- 7 x y$ .

$5 - 42 y + 7 x y - 7 x y = 14 x$

Subtract $7 x y$ from $7 x y$ .

$5 - 42 y + 0 = 14 x$

Add $5 - 42 y$ and $0$ .

$5 - 42 y = 14 x$

Subtract $5$ from both sides of the equation.

$- 42 y = 14 x - 5$

Divide each term in $- 42 y = 14 x - 5$ by $- 42$ and simplify.

Divide each term in $- 42 y = 14 x - 5$ by $- 42$ .

$\frac{- 42 y}{- 42} = \frac{14 x}{- 42} + \frac{- 5}{- 42}$

Simplify the left side.

Cancel the common factor of $- 42$ .

Cancel the common factor.

$\frac{- 42 y}{- 42} = \frac{14 x}{- 42} + \frac{- 5}{- 42}$

Divide $y$ by $1$ .

$y = \frac{14 x}{- 42} + \frac{- 5}{- 42}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $14$ and $- 42$ .

Factor $14$ out of $14 x$ .

$y = \frac{14 (x)}{- 42} + \frac{- 5}{- 42}$

Cancel the common factors.

Factor $14$ out of $- 42$ .

$y = \frac{14 x}{14 \cdot - 3} + \frac{- 5}{- 42}$

Cancel the common factor.

$y = \frac{14 x}{14 \cdot - 3} + \frac{- 5}{- 42}$

Rewrite the expression.

$y = \frac{x}{- 3} + \frac{- 5}{- 42}$

Move the negative in front of the fraction.

$y = - \frac{x}{3} + \frac{- 5}{- 42}$

Dividing two negative values results in a positive value.

$y = - \frac{x}{3} + \frac{5}{42}$

Step 2

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be $0$ or $1$ for each of its variables. In this case, the degree of variable $y$ is $1$ and the degree of variable $x$ is $1$ .

Linear

Determine if Linear 7x(y+2)=5-7y(6-x)

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