The Understanding systems of equations word problems exercise appears under the 8th grade (U.S.) Math Mission and Algebra I Math Mission. This exercise is a culminating task on dealing with systems of equations algebraically and graphically.
Types of Problems
There are three types of problems in this exercise:
- Interpret the information to solve the system: This problem describes a situation that can be solved with a system of equations. The student is asked to solve the system and select the most appropriate answer from a multiple choice list.
- Understand how many solutions you can have: These problems test the student's ability to realize how many times lines can intersect.
- Understand how graph determines number of solutions: This problem provides a situation and the student is asked to determine which of the graphs could be an illustration of that situation.
Strategies
Confidence with linear equations in graphing, algebraic and numerical senses would ensure success on this exercise.
- Lines that cross each other have a single solution.
- Lines that are coincident (completely overlap) have infinitely many solutions.
- Lines that are parallel have no solutions.
- Lines that intersect in three places (or more) automatically intersect in infinitely many places.
- If a system cannot be solved, then the particular values of a system cannot be determined.
Real-life applications
- Systems of equations are used to solve some mixture problems in chemistry.
- Systems of equations are used to solve distance, rate, time problems in physics.
- Systems of equations can be used with certain Cost and Revenue situations to find break-even points.
- Systems of equations can be used with supply and demand to find equilibrium prices.
- Being able to determine if and when a system has a solution can help in applications in the sciences to understand if more information or data needs to be collected.