Solve any system of two linear equations

The  exercise appears under the Algebra I Math Mission. This exercise practices solving systems of equations with any number of solutions using any solution method.

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


 * 1) Determine the number of solutions, if one type the values: This problem provides a system of two equations in two unknowns. The student is expected to determine whether the system has none, one or infinitely many solutions. If the system has one, the student is asked to type the $$x$$ and $$y$$ values of the solution. Solve any system of two linear equations.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.