Systems with one, zero, or infinite solutions

The  exercise appears under the 8th Grade Math Mission. This exercise strengthens the relationship between the equations of lines and how many solutions a particular system has.

Types of Problems
There is one type of problem in this exercise:


 * 1) Tell how many solutions exist: This problem provides a system of two equations in two unknowns. The student is asked to determine whether the system has none, one or infinitely many solutions.Swozois1.png

Strategies
Algebraic skills to manipulate algebraic forms are valuable here, as is the process of elimination. They are not necessary to complete the exercise, but can aid in efficiency.
 * 1) Lines that are not parallel have a single solution.
 * 2) Lines that have the same slope and y-intercept have infinitely many solutions.
 * 3) Lines that have the same slope but different y-intercepts parallel have no solutions.

Real-life applications

 * 1) Systems of equations are used to solve some mixture problems in chemistry.
 * 2) Systems of equations are used to solve distance, rate, time problems in physics.
 * 3) Systems of equations can be used with certain Cost and Revenue situations to find break-even points.
 * 4) Systems of equations can be used with supply and demand to find equilibrium prices.