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A graph is given below whose equation is $2 x − 3 y = 4$ . State true or false for the following statement by verifying theoretically and by observing the graph.

$x = − 1, y = − 2$ is a solution of the given equation.

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True

False

answer is A.

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Detailed Solution

Given equation is

2 x − 3 y = 4

The equation is written in terms of x,

⇒ − 3 y = 4 − 2 x ⇒ y = − (4 − 2 x) 3 ⇒ y = (2 x − 4) 3

When

x = − 1

, y becomes,

⇒ y = 2 (− 1) − 4 3 ⇒ y = − 2 − 4 3 ⇒ y = − 6 3 ⇒ y = − 2

The point is

(− 1, − 2)

.
Therefore, the point

(− 1, − 2)

is a solution of the equation

2 x − 3 y = 4

.
We can observe from the graph that this point coincides with the given line.
Hence, the statement is true. So, option 1 is correct.

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