Google Classroom
GeoGebraGeoGebra Classroom

1.1: Solving Systems of Equations with Parameters (E1)

Exercise

Suppose we are given the following system of equations to solve, and we want to let z be our parameter: (1) (2)

Moving the z slider below, we see that we are solving for the solution in terms of z, so that if we pick a value for z, we plug in that value to get the solution to these two equations.

The Game Plan:

To solve this type of question, we want to leave and in terms of . So we will use the Echelon Method to solve this system, and our answer should contain 's in the and solution.

Solution

Solution

From this graph, we see that each equation, and therefore, each solution, is affected by the value of z.