Question

The condition that the equation ax + by + c = 0 represents a linear equation is two variables is
(a) a ≠ 0,b = 0 (b) b ≠ 0, a = 0 (c) a = 0, b = 0 (d) a ≠ 0, b ≠ 0

Answer 1

Option D) a ≠ 0, b ≠ 0

Step-by-step explanation:

We are given the following in the question:

Linear equation in two variables:

$ax + by + c = 0$

(a) a ≠ 0,b = 0

The equation becomes

$ax + c = 0$

which is not a linear equation in two variables.

(b) b ≠ 0, a = 0

$by + c = 0$

which is not a linear equation in two variables.

(c) a = 0, b = 0

The equation becomes

$c = 0$

which is not a linear equation in two variables.

(d) a ≠ 0, b ≠ 0

Thus, this is the appropriate condition for an equation to be a linear equation in two variable.

Option D) a ≠ 0, b ≠ 0

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Answer 2

Answer:

Step-by-step explanation:

Option D) a ≠ 0, b ≠ 0

Step-by-step explanation:

We are given the following in the question:

Linear equation in two variables:

(a) a ≠ 0,b = 0

The equation becomes

which is not a linear equation in two variables.

(b) b ≠ 0, a = 0

which is not a linear equation in two variables.

(c) a = 0, b = 0

The equation becomes

which is not a linear equation in two variables.

(d) a ≠ 0, b ≠ 0

Thus, this is the appropriate condition for an equation to be a linear equation in two variable.

Option D) a ≠ 0, b ≠ 0

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