Question

The age of ‘x’ is more than the age of ‘y’ by 10 years
i) Express this statement in linear equations in two variables.
ii) Also express it in the form ax+by+c=0 and indicate the value of a,b,c.

Answer 1

Hint: The given statement involves ages of two different persons. It says the age of one person is more by 10 years than the other. We will introduce the age of one person as a variable ‘x’ and the age of another person as a variable ‘y’ and then proceed further with the statement to make a linear equation.

Complete step-by-step answer:
The given statement is:
The age of ‘x’ is more than the age of ‘y’ by 10 years
Clearly the statement means that ‘x’ is older than ‘y’ by ten years.
Let the age of ‘x’ be x-years and the age of ‘y’ be y-years.
So mathematically we have,
 $ x=y+10 $ --(1)
This is the answer to the first part (i).
For the second part we have to reduce (1) to the form ax+by+c=0
 $ \Rightarrow x=y+10 $
subtracting (y+10) on both sides of the equations we have,
 $ \Rightarrow x-(y+10) =y+10-(y+10) $
The right hand side become zero so now we have
 $ \Rightarrow x-(y+10) =0 $
or we can write it as,
 $ \Rightarrow x-y-10=0 $
Comparing this to ax+by+c=0 we get,
a=1,b=-1,c=-10
The above is the solution to part (ii)
So, the correct answer is “a=1,b=-1,c=-10”.

Note: : Always read the statement carefully. It contains important information and half of the solution. After reading the statement use the variables as ‘x’,’y’ or ‘z’ instead of ‘a’,’b’,’c’ as it can lead to confusion on solving the second part.