Question

1: Create a single variable linear equation that has no solution. Solve the equation algebraically to prove that it does not have a solution.
2: 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.
3: 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

Answer 1

Answer:

(1) y=C, $C\neq0$

(2) x=C

(1) y=0

Step-by-step explanation:

For the linear equation, the power on the solitary variable must be 1.

When the graph of a function crosses/ touches the x-axis than the equation has solution/solutions otherwise it does not has a solution.

When it touches/cresses the x-axis for infinite times then it will have an infinite number of solutions.

(1) The linear equation y-C=0, where y is a variable and C is a non-zero constant,  $C \neq 0$, has the graph parallel to the x-axis. It has no solution as the graph will never cross/touch the x-axis.

Algebraically, in linear equation y-C=0, is independent of x, so there is no value of x for the solution to be exist.

(2) The linear equation x-C=0, where x is a variable and C is a constant, has one solution.

The solution for the equation is

x-C=0

$\Rightarrow x=C$, where $C\neq0$.

(3) The linear equation y=0, where y is a variable, has the graph coinciding with the x-axis. So, it has infinitely many solutions.

Algebraically, in linear equation y=0, is independent of x, so for all value of x, the given equation is zero. Hence, there are infinitely many solutions.