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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)
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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