Question

How can you write an equation in two variables to solve a problem?

Answer 1

Hint: First identify the unknown quantity and hence assign a variable to them. Now analyze all the given conditions and try to write each term of the equation. Hence writing all the conditions given in the problem we will form the required equation in two variables

Complete step by step solution:
Now any problem can be written in a mathematical form. We call this an equation. Now to write an equation let us first understand the terms used to write the equation.
First let us understand what variables are.
Now variables are generally the unknown quantities. The first step of writing an equation is identifying the variables. Suppose we have a quantity and we do not know the value of the quantity then we assume the quantity to be a variable which can be represented by any small alphabet.
Now the whole purpose of the equation is to find the unknown quantity.
Hence what we assume the quantity to be is let's say x. Now we will write the required conditions and hence form an equation.
Now let us understand constants. Constants are all the numbers which are constant throughout the equation. Hence the fixed quantities are represented by constants.
Now if a constant is multiplied to a variable then we call it as a coefficient.
Now we will try to form an equation by taking an example.
Let us say we are given Age of Person A is 5 more than twice the age of person B.
Now let us analyze the expression.
Here we have two unknown quantities, which are age of A and age of B.
Hence let us say age of A is x and age of B is y.
Now we have 2 constants which are 5 and 2.
Now twice the age of person B is nothing but $2\times y=2y$
Now let us write 5 more than twice the age of B. we know we use addition to express more in Math.
Hence we have 2y+5
But what is 5 more than twice the age of person B. It is age of person A which is x.
Hence we have x=2y+5
Now since the equation has two variables we call it as an equation in two variables.

Note: Now note that while writing such equations always break the sentences and write each term properly. Just like in the above problem. Now two times or twice always denotes the coefficient related to variables. While 5 more or 5 less these types of words represent constants.