Analyze the solutions of systems of equations algebraically

The  exercise appears under the Algebra I Math Mission. This exercise practices determining the number of solutions of a given system of equations by considering its algebraic solution process.

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


 * 1) Determine the number of solutions: 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.Analyze the solutions of systems of equations algebraically.PNG

Strategies
Algebraic skills to manipulate algebraic forms are useful for success while doing this exercise.
 * 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.