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ax + by + c = 0, where a, b and c are real numbers, is a linear equation in two variables. Is the given statement true or false? Justify your answer

Solution:

We know that

ax + by + c = 0, where a, b and c are real numbers is a linear equation in two variables only if a and b are non-zero

Therefore, the statement is false.

✦ Try This: The graph of the linear equation 6x + 5y = 30 is a line which meets the x-axis at the point a. (0, 6), b. (6, 0), c. (5, 0), d. (0, 5)

An equation that has the highest degree of 1 is known as a linear equation.

It means that no variable in a linear equation has an exponent more than 1.

The given linear equation is 6x + 5y = 30

It meets the x-axis which means that y = 0

Let us substitute it in the equation

6x + 5(0) = 30

6x = 30

Dividing both sides by 6

x = 5

Therefore, the graph of the linear equation is (5, 0).

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

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

ax + by + c = 0, where a, b and c are real numbers, is a linear equation in two variables. Is the given statement true or false? Justify your answer

Summary:

The statement “ax + by + c = 0, where a, b and c are real numbers, is a linear equation in two variables” is false. It is possible only if a and b are non-zero

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