Question

7. The linear equation 3x - 5y = 15 has
(a) a unique solution
(b) two solutions
(c) infinitely many solutions (d) no solution​

Answer 1

(c) infinitely many solutions

The linear equation 3x - 5y = 15 has infinitely many solutions.

Step-by-step explanation:

The given linear equation is 3x - 5y = 15

When x = 0, we have

3 (0) - 5y = 15

⇒ 0 - 5y = 15

⇒ 5y = - 15

⇒ y = - 3

So, x = 0, y = - 3 is a solution.

When x = 1, we have

3 (1) - 5y = 15

⇒ 3 - 5y = 15

⇒ 5y = - 12

⇒ y = - 12/5

So, x = 1, y = - 12/5 is a solution.

When x = 2, we have

3 (2) - 5y = 15

⇒ 6 - 5y = 15

⇒ 5y = - 9

⇒ y = - 9/5

So, x = 2, y = - 9/5 is a solution.

In this way, we can find infinitely many solutions that satisfy the given linear equation.

NOTE:

The given linear equation 3x - 5y = 15 represents a straight line that intersects both the axes. We can find infinitely many points that lie on the straight line.

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