Solved on Jan 24, 2024

Determine if the equation $7x(y+2) = 3 - 7y(10-x)$ is linear or not linear.

STEP 1

Assumptions
1. We are given the equation $7x(y+2) = 3 - 7y(10-x)$ .
2. We need to determine whether this equation is linear or not.

STEP 2

To determine if the equation is linear, we need to check if the equation can be written in the form $Ax + By + C = 0$ , where $A$ , $B$ , and $C$ are constants.

STEP 3

First, we will expand both sides of the given equation to eliminate the parentheses.
$7x(y+2) = 3 - 7y(10-x)$

STEP 4

Expand the left side of the equation.
$7xy + 14x = 3 - 7y(10-x)$

STEP 5

Expand the right side of the equation.
$7xy + 14x = 3 - 70y + 7yx$

STEP 6

Combine like terms. Notice that $7xy$ and $7yx$ are like terms since they represent the same product of $x$ and $y$ .
$7xy + 14x = 3 - 70y + 7xy$

STEP 7

Subtract $7xy$ from both sides to move all terms involving variables to one side.
$7xy + 14x - 7xy = 3 - 70y + 7xy - 7xy$

STEP 8

Simplify both sides of the equation.
$14x = 3 - 70y$

STEP 9

Now we have an equation in the form $Ax + By + C = 0$ , where $A = 14$ , $B = -70$ , and $C = -3$ .

STEP 10

Since the equation can be written in the form $Ax + By + C = 0$ and $A$ , $B$ , and $C$ are constants, the equation is linear.
The equation $7x(y+2) = 3 - 7y(10-x)$ is linear.

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Determine if the equation $7x(y+2) = 3 - 7y(10-x)$ is linear or not linear.

STEP 1

Assumptions
1. We are given the equation $7x(y+2) = 3 - 7y(10-x)$ .
2. We need to determine whether this equation is linear or not.

STEP 2

To determine if the equation is linear, we need to check if the equation can be written in the form $Ax + By + C = 0$ , where $A$ , $B$ , and $C$ are constants.

STEP 3

First, we will expand both sides of the given equation to eliminate the parentheses.
$7x(y+2) = 3 - 7y(10-x)$

STEP 4

Expand the left side of the equation.
$7xy + 14x = 3 - 7y(10-x)$

STEP 5

Expand the right side of the equation.
$7xy + 14x = 3 - 70y + 7yx$

STEP 6

Combine like terms. Notice that $7xy$ and $7yx$ are like terms since they represent the same product of $x$ and $y$ .
$7xy + 14x = 3 - 70y + 7xy$

STEP 7

Subtract $7xy$ from both sides to move all terms involving variables to one side.
$7xy + 14x - 7xy = 3 - 70y + 7xy - 7xy$

STEP 8

Simplify both sides of the equation.
$14x = 3 - 70y$

STEP 9

Now we have an equation in the form $Ax + By + C = 0$ , where $A = 14$ , $B = -70$ , and $C = -3$ .

STEP 10

Since the equation can be written in the form $Ax + By + C = 0$ and $A$ , $B$ , and $C$ are constants, the equation is linear.
The equation $7x(y+2) = 3 - 7y(10-x)$ is linear.

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Determine if the equation 7x(y+2)=3−7y(10−x)7x(y+2) = 3 - 7y(10-x)7x(y+2)=3−7y(10−x) is linear or not linear.

STEP 1

Assumptions1. We are given the equation 7x(y+2)=3−7y(10−x)7x(y+2) = 3 - 7y(10-x)7x(y+2)=3−7y(10−x).2. We need to determine whether this equation is linear or not.

STEP 2

To determine if the equation is linear, we need to check if the equation can be written in the form Ax+By+C=0Ax + By + C = 0Ax+By+C=0, where AAA, BBB, and CCC are constants.

STEP 3

First, we will expand both sides of the given equation to eliminate the parentheses.7x(y+2)=3−7y(10−x)7x(y+2) = 3 - 7y(10-x)7x(y+2)=3−7y(10−x)

STEP 4

Expand the left side of the equation.7xy+14x=3−7y(10−x)7xy + 14x = 3 - 7y(10-x)7xy+14x=3−7y(10−x)

STEP 5

Expand the right side of the equation.7xy+14x=3−70y+7yx7xy + 14x = 3 - 70y + 7yx7xy+14x=3−70y+7yx

STEP 6

Combine like terms. Notice that 7xy7xy7xy and 7yx7yx7yx are like terms since they represent the same product of xxx and yyy.7xy+14x=3−70y+7xy7xy + 14x = 3 - 70y + 7xy7xy+14x=3−70y+7xy

STEP 7

Subtract 7xy7xy7xy from both sides to move all terms involving variables to one side.7xy+14x−7xy=3−70y+7xy−7xy7xy + 14x - 7xy = 3 - 70y + 7xy - 7xy7xy+14x−7xy=3−70y+7xy−7xy

STEP 8

Simplify both sides of the equation.14x=3−70y14x = 3 - 70y14x=3−70y

STEP 9

Now we have an equation in the form Ax+By+C=0Ax + By + C = 0Ax+By+C=0, where A=14A = 14A=14, B=−70B = -70B=−70, and C=−3C = -3C=−3.

STEP 10

Since the equation can be written in the form Ax+By+C=0Ax + By + C = 0Ax+By+C=0 and AAA, BBB, and CCC are constants, the equation is linear.The equation 7x(y+2)=3−7y(10−x)7x(y+2) = 3 - 7y(10-x)7x(y+2)=3−7y(10−x) is linear.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Determine if the equation $7x(y+2) = 3 - 7y(10-x)$ is linear or not linear.

Assumptions
1. We are given the equation $7x(y+2) = 3 - 7y(10-x)$ .
2. We need to determine whether this equation is linear or not.

To determine if the equation is linear, we need to check if the equation can be written in the form $Ax + By + C = 0$ , where $A$ , $B$ , and $C$ are constants.

First, we will expand both sides of the given equation to eliminate the parentheses.
$7x(y+2) = 3 - 7y(10-x)$

Expand the left side of the equation.
$7xy + 14x = 3 - 7y(10-x)$

Expand the right side of the equation.
$7xy + 14x = 3 - 70y + 7yx$

Combine like terms. Notice that $7xy$ and $7yx$ are like terms since they represent the same product of $x$ and $y$ .
$7xy + 14x = 3 - 70y + 7xy$

Subtract $7xy$ from both sides to move all terms involving variables to one side.
$7xy + 14x - 7xy = 3 - 70y + 7xy - 7xy$

Simplify both sides of the equation.
$14x = 3 - 70y$

Now we have an equation in the form $Ax + By + C = 0$ , where $A = 14$ , $B = -70$ , and $C = -3$ .

Since the equation can be written in the form $Ax + By + C = 0$ and $A$ , $B$ , and $C$ are constants, the equation is linear.
The equation $7x(y+2) = 3 - 7y(10-x)$ is linear.