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The linear equation $2 x + 5 y = 7$ has:

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a unique solution

two solutions

three solutions

infinitely many solutions

answer is D.

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Detailed Solution

Given a linear equation:

2 x + 5 y = 7

........(1)
Any equation which can be put in the form

a x + b y + c = 0

, where a, b and c are real numbers, and a and b are not zero, is called a linear equation in two variables.

2 x + 5 y = 7

is a single equation involving two variables.
For any value of x, there is a value for y and vice-versa.
Let us assume value of x=1

21 + 5 y = 7 2 + 5 y = 7 5 y = 7 − 2 5 y = 5 y = 1

substitute the value of y=1 in (1)

21 + 51 = 7 2 + 5 = 7 7 = 7

The given equation has same graph for any value.
Therefore 2 x+5 y=7 has an infinite number of solutions.
Therefore, the correct option is 4.

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