Question

Hema’s age is 4 times the age of Mary. Write a linear equation in two variables to represent this information.

Answer 1

Hint:
To represent this information as a linear equation in two variables, we will try to understand the given sentence in our own words and then think of the mathematical representation of the given sentence. After stating the mathematical representation, we would compare the linear equation with the general form of linear equation in two variables and we would find our required equation.

Complete step by step solution:
We have to represent the given equation in a linear equation in two variables. Hence, we should know what exactly a linear equation in two variable means.
An equation is called linear equation in two variables if it can be written in the form of \[ax + by + c = 0\] where \[a,b,c\] are real numbers and \[a \ne 0\] , \[b \ne 0\] as they are coefficients of \[x\] and \[y\] respectively. There are two variables \[x\] and \[y\], Also, their power will be 1 as it is a ‘linear equation’. Linear equation in two variables can have infinitely many solutions rather than only one in the case of ‘one variable’.
Let Hema’s age be \[x\]years and Mary’s age be \[y\] years.
We have let their ages equal to two variables because we are required to form a linear equation in two variables i.e in the form of \[ax + by + c = 0\]
Now, the question states that Hema’s age is 4 times the age of Mary.
But as we have let their ages equal to two variables, hence, we can rewrite this sentence by substituting Hema’s age by \[x\]years and Mary’s age by \[y\] years. Also, it is given that Hema’s age ‘is 4 times’ the age of Mary which means that we can equate their ages as:
\[x = 4y\]
Now, subtracting \[4y\] from both the sides, we get,
\[x - 4y = 0\] , which is the required linear equation in two variables because it is of the form \[ax + by + c = 0\]
Here,
 \[a = 1,b = - 4\]
And,
\[c = 0\]

Hence, to represent the given information, the required linear equation in two variables is:
\[x - 4y = 0\]

Note:
To answer this question we should know how to represent given information, mathematically. Also, understanding the meaning of the question plays an important role in such types of questions because if for example, we understood the meaning incorrectly then we could write the equation as \[4x = y\], hence, making our equation completely wrong.