What Does It Mean When An Equation Has No Solution?

What Does It Mean When An Equation Has No Solution?

Note:

Sometimes equations have no solution. This means that no matter what value is plugged in for the variable, you will ALWAYS get a contradiction. Watch this tutorial and learn what it takes for an equation to have no solution.

Keywords:

problem

untrue

variable

contradiction

unequal sides

false

never true

no solution

no value

different sides

not equal

right side

left side

sides never equal

group variables

variables cancel

Background Tutorials

Interpret parts of an expression, such as terms, factors, and coefficients.

You can't do algebra without working with variables, but variables can be confusing. If you've ever wondered what variables are, then this tutorial is for you!

Further Exploration

Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

Trying to solve an equation with variables on both sides of the equation? Figure out how to get those variables together and solve the equation with this tutorial! Surprise! Turns out, this equation has no solution. Check out this tutorial and see why!

Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.

There are many different ways to solve a system of linear equations. In this tutorial, you'll see how to solve a system of linear equations by graphing both lines and finding their intersection. Take a look!