Equations can have one solution, more than one solution or none at all.
- <em>The equation is an identity when the missing value is 8</em>
- <em>The equation cannot have exactly one solution</em>
- <em>The equation has exactly one solution when the missing value is anything except 8</em>
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The equation is given as:
Represent the blank with y.
So, we have:
<u>(a) The missing value when the equation is an identity equation</u>
To do this, we simply solve for y in
Open brackets
Collect like terms
Divide both sides by 2
Hence, the equation is an identity when the missing value is 8
<u>(b) The missing value when the equation has one solution</u>
In (a), we have:
For the equation to have one solution, variable x must be on either sides of the equation.
i.e. or
, where
Since x has been eliminated, then the equation can not have one solution.
<u>(c) The missing value when the equation has no solution</u>
In (a), we have:
This means that the equation will have no solution when the missing value is not 8
i.e.
Read more about equations at: