Question

Tom found that a linear equation with one variable (the variable x) can be transformed into an equivalent equation that has no solutions. Which of the following would show that the linear one–variable equation has no solution?

0 = 1
x = 0
0 = 0
x = 1

Answer 1

A linear one-variable equation can have no solution if its left-hand side (LHS) is not equal to its right-hand side (RHS). In other words, if the equation simplifies to a statement that is always false, then the equation has no solution.

Step-by-step explanation:

A linear equation with one variable has no solutions when it can be transformed into an equation that states a logically impossible equality, like 0 = 1.

Let's analyze each option:

1. 0 = 1: This statement is logically false. Zero will never equal one, regardless of the value of x. Therefore, if a linear equation can be transformed into this equation, it has no solutions.

2. x = 0: This statement only specifies a single solution for x, namely 0. However, it doesn't necessarily indicate that the equation has no solutions.

3. 0 = 0: This statement is always true. It doesn't provide any information about the solutions of the original equation.

4. x = 1: Like option 2, this statement only specifies a single solution for x, namely 1.

Therefore, the only option that shows the linear one-variable equation has no solution is 0 = 1.

Answer 2

0=1

Step-by-step explanation:

0=1 is not equal