Question

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

Answer 1

Hint:
1) Use some two variables like x and y, a and b, p and q etc. to represent the values of Hema's age and Mary's age separately.
2) Use the given relation between the values to form an equation.
3) A linear equation has degree 1. i.e. the maximum power of a variable in it is 1, when it is converted into a form where variables are free of radicals and rational expressions.

Complete step by step solution:
Let us say that Hema's age is x years and Mary's age is y years.
According to the question, Hema's age is four times the age of Mary.
i.e. $\text{Age of Hema}=4\times \left(\text{Age of Mary}\right)$ .
Four times Mary's age will be $4\times y=4y$ years.
Therefore, we get the following equation:
 $x=4y$

Since the degree of the expressions on either side of the equation is 1, it is the required linear equation.

Note:
1) The degree of terms involving a product of variables is NOT 1.
e.g. $xy$ has degree 2, $x{{y}^{2}}z$ has degree 4 etc.
2) Polynomials of degree one, two or three are respectively linear polynomials, quadratic polynomials and cubic polynomials. For higher degrees, the specific names are not commonly used, although quartic polynomial (for degree four) and quintic polynomial (for degree five) are sometimes used.
3) The names for the degrees may be applied to the polynomial or to its terms.
For example, the term $2x$ in ${{x}^{2}}+2x+3$ is a linear term in a quadratic polynomial.
4) A polynomial of degree zero is a constant polynomial, or simply a constant.