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A linear equation 2x + 3y = 5 has a unique solution. Is the given statement true or false? Justify your answer

Solution:

The given linear equation is 2x + 3y = 5

We can write it as

3y = 5 - 2x

Dividing both sides by 3

y = 5/3 - 2x/3

Here y takes many values infinitely many solutions for various x values

Therefore, the statement is false.

✦ Try This: If (3, 0) is a solution of the linear equation 2x + 8y = 16k, then the value of k is a. 4, b. 6, c. 5, d. 8/3

The given linear equation is

2x + 8y = 16k

The point given here is

(x, y) = (3, 0)

Let us substitute the given values in the equation

2 (3) + 8(0) = 16k

By further calculation

6 + 0 = 16k

So we get

k = 16/6

k = 8/3

Therefore, the value of k is 8/3.

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

NCERT Exemplar Class 9 Maths Exercise 4.2 Sample Problem 1(ii)

A linear equation 2x + 3y = 5 has a unique solution. Is the given statement true or false? Justify your answer

Summary:

An equation that has the highest degree of 1 is known as a linear equation. The statement “A linear equation 2x + 3y = 5 has a unique solution” is false

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