Determine if Linear 10x(y+4)=11-10y(9-x)

$10 x (y + 4) = 11 - 10 y (9 - x)$

Step 1

Solve the equation for $y$ .

Simplify $10 x (y + 4)$ .

Rewrite.

$0 + 0 + 10 x (y + 4) = 11 - 10 y (9 - x)$

Simplify by adding zeros.

$10 x (y + 4) = 11 - 10 y (9 - x)$

Apply the distributive property.

$10 x y + 10 x \cdot 4 = 11 - 10 y (9 - x)$

Multiply $4$ by $10$ .

$10 x y + 40 x = 11 - 10 y (9 - x)$

Simplify each term.

Apply the distributive property.

$10 x y + 40 x = 11 - 10 y \cdot 9 - 10 y (- x)$

Multiply $9$ by $- 10$ .

$10 x y + 40 x = 11 - 90 y - 10 y (- x)$

Rewrite using the commutative property of multiplication.

$10 x y + 40 x = 11 - 90 y - 10 \cdot - 1 y x$

Multiply $- 10$ by $- 1$ .

$10 x y + 40 x = 11 - 90 y + 10 y x$

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

$11 - 90 y + 10 y x = 10 x y + 40 x$

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

Subtract $10 x y$ from both sides of the equation.

$11 - 90 y + 10 y x - 10 x y = 40 x$

Combine the opposite terms in $11 - 90 y + 10 y x - 10 x y$ .

Reorder the factors in the terms $10 y x$ and $- 10 x y$ .

$11 - 90 y + 10 x y - 10 x y = 40 x$

Subtract $10 x y$ from $10 x y$ .

$11 - 90 y + 0 = 40 x$

Add $11 - 90 y$ and $0$ .

$11 - 90 y = 40 x$

Subtract $11$ from both sides of the equation.

$- 90 y = 40 x - 11$

Divide each term in $- 90 y = 40 x - 11$ by $- 90$ and simplify.

Divide each term in $- 90 y = 40 x - 11$ by $- 90$ .

$\frac{- 90 y}{- 90} = \frac{40 x}{- 90} + \frac{- 11}{- 90}$

Simplify the left side.

Cancel the common factor of $- 90$ .

Cancel the common factor.

$\frac{- 90 y}{- 90} = \frac{40 x}{- 90} + \frac{- 11}{- 90}$

Divide $y$ by $1$ .

$y = \frac{40 x}{- 90} + \frac{- 11}{- 90}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $40$ and $- 90$ .

Factor $10$ out of $40 x$ .

$y = \frac{10 (4 x)}{- 90} + \frac{- 11}{- 90}$

Cancel the common factors.

Factor $10$ out of $- 90$ .

$y = \frac{10 (4 x)}{10 (- 9)} + \frac{- 11}{- 90}$

Cancel the common factor.

$y = \frac{10 (4 x)}{10 \cdot - 9} + \frac{- 11}{- 90}$

Rewrite the expression.

$y = \frac{4 x}{- 9} + \frac{- 11}{- 90}$

Move the negative in front of the fraction.

$y = - \frac{4 x}{9} + \frac{- 11}{- 90}$

Dividing two negative values results in a positive value.

$y = - \frac{4 x}{9} + \frac{11}{90}$

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 10x(y+4)=11-10y(9-x)

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