Question

)Write an equation that has one solution, an equation that has no solution,

and an equation that has infinitely many solutions.

Answer 1

A linear equation can have no, one or infinite solutions.

Explanation:

No Solution:

Consider the equation 8x - 19 = 8x + 19

Subtract 8x from both the sides. We get:

8x - 8x - 19 = 8x - 8x + 19

⇒ - 19 = 19

This is absurd. So, this system of equations has no solution.

One Solution:

For the equation 9x + 5 = 14

⇒ 9x = 9

⇒ x = 1 the only solution to the equation.

Infinite Solutions:

The solution to the equation 3x = 3x are infinite.

Whatever the value of x the equation always remains the same. So, we have infinite values of x that can satisfy the equation.