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#13

create a single variable linear equation that has no solution. solve the equation algebraically to prove that it does not have a solution.
create a single variable linear equation that has one solution. solve the equation algebraically to prove that there is one distinct solution for the equation.
create a single variable linear equation that has infinitely many solutions. solve the equation algebraically to prove that there is an infinite number of solutions for the equation

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

Step-by-step 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.

no

step-by-step explanation:

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