| Analyze the solutions of systems of equations algebraically | |
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| Description | |
| Exercise Name: | Analyze the solutions of systems of equations algebraically |
| Math Missions: | Algebra I Math Mission, Mathematics II Math Mission |
| Types of Problems: | 1 |
The Analyze the solutions of systems of equations algebraically exercise appears under the Algebra I Math Mission and Mathematics II 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:
- 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.
Determine the number of solutions
Strategies[]
Algebraic skills to manipulate algebraic forms are useful for success while doing this exercise.
- Lines that are not parallel have a single solution.
- Lines that have the same slope and y-intercept have infinitely many solutions.
- Lines that have the same slope but different y-intercepts parallel have no solutions.
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.