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The Linear equations with one, zero, or infinite solutions exercise appears under the 8th grade (U.S.) Math Mission, Algebra I Math Mission and Mathematics II Math Mission. This exercise helps to understand the difference between equations with one solution, no solutions and many solutions.

## Types of Problems

There are three types of problems in this exercise:

1. Tell how many solutions the equation has: This problem has an equation and the user is asked to determine how many solutions the equation has.
2. Insert values to make a type of equation: This problem provides an equation with blanks and the users are asked to fill in the blanks to make a certain type of equation.
3. Tell which value could make a type of equation: This problem provides an equation with a blank and asks the user to select the answer from a multiple choice list that makes an equation of a particular type.
4. Drop-down to make the type of equation: This problem provides a template for an equation with drop-down menus for some values. The user is asked to select the correct options to make a certain type of equation.

## Strategies

Knowledge of identities and contradictions helps to perform this problem accurately and efficiently.

1. Equations should be solved in the standard way. If ${x}$ can be isolated, there is one solution. If the ${x}$s are reduced completely and what remains is a true statement, then there are infinitely many solutions. If the ${x}$s reduce and all that remains is a false statement, then there are no solutions.

## Real-life Aplications

1. Ability to work well with lines is an advantage in calculus as tangent lines are approximations to curved objects.
2. An ability to recognize identities and contradictions can help with logic and reasoning in debate and critical thinking.
3. The SAT has problems of this type.
4. Equations show up in nearly every science or business class one is ever in.
5. Computers are also equation solvers. Computers were originally invented to solve equations over and over again instead of humans doing the calculations.
6. Knowledge of algebra is essential for higher math levels like trigonometry and calculus. Algebra also has countless applications in the real world.