The equation 2x + 5y = 7 has a unique solution, if x, y are
a. Natural numbers
b. Positive real numbers
c. Real numbers
d. Rational numbers

Solution:

The given equation is

2x + 5y = 7

Let us consider the value (1, 1)

a. The solution of 2x + 5y = 7 is (1, 1)

b. 2x + 5y = 7 will have many solutions if positive real numbers are considered

c. 2x + 5y = 7 will have infinitely many solutions if real numbers are considered

d. 2x + 5y = 7 will have many solutions if rational numbers are considered

We know that

A linear equation in two variables has infinitely many solutions.

For the linear equations system, there is a solution set of infinite points for which the L.H.S of an equation becomes R.H.S.

Therefore, the equation has a unique solution if x, y are natural numbers.

✦ Try This: The equation 6x + 3y = 12 has a unique solution, if x, y are : a. Natural numbers, b. Positive real numbers, c. Real numbers, d. Rational numbers

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 4

NCERT Exemplar Class 9 Maths Exercise 4.1 Problem 2

The equation 2x + 5y = 7 has a unique solution, if x, y are a. Natural numbers, b. Positive real numbers, c. Real numbers, d. Rational numbers

Summary:

The standard form of linear equations in two variables is expressed as, Ax + By = C; where A, B and C are integers, and x and y are the variables. The equation 2x + 5y = 7 has a unique solution, if x, y are natural numbers

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