Question

Solve for x: z(14x−2y)=7 if z equals 0 Solve for x: z(14x−2y)=7 if z does not equal 0

Answer 1

• 
  `z = 0`; x doesn't have a solution

• 
  `z\\eq 0`;
  `x = (1)/(14)((7)/(z) + 2y)`

Explanation:

Given

`z(14x -2y)=7`

Required;

Solve for x, when

• 
  `z = 0`

• 
  `z\\eq 0`

`z(14x -2y)=7`

Divide both sides by z

`(z(14x -2y))/(z) = (7)/(z)`

`14x -2y = (7)/(z)`

Add 2y to both sides

`14x -2y + 2y= (7)/(z) + 2y`

`14x = (7)/(z) + 2y`

Divide both sides by 14

`(14x)/(14) = (1)/(14)((7)/(z) + 2y)`

`x = (1)/(14)((7)/(z) + 2y)`

The above expression is the value of x when
`z\\eq 0`

To solve for when z = 0, we simply substitute 0 for z

`x = (1)/(14)((7)/(z) + 2y)`

`x = (1)/(14)((7)/(0) + 2y)`

0 cant't divide any number; hence, from the above expression we conclude that

`x = \ u\ n\ d\ e \ f\ i \ n\ e\ d`

or

x doesn't have a solution