1. Is (2, 3) a solution of the system ?
a. For a system of two linear equations in two variables, explain, in geometric terms, each of the following: dependent system of equations, inconsistent system of equations, independent system of equations.
b. Write three different systems of equations: (a) one that has the point (1, 1) as its only solution, (b) one for which there is no solution, and (c) one that has infinite number of solutions.
3. Solve the following systems algebraically and describe the nature of the solution if it exists.
a. b. c.
4. Solve the following systems algebraically and describe the nature of the solution if it exists.
a. b. c.
5. The following was offered as a solution to the system of equations .
Step 1. Substitute for y:
Step 2. Solve for x:
At this point the student stated that because , the system of equations has no solution. If this assertion is correct, is the system of equations independent, dependent, or inconsistent? If the assertion is not correct, what is the correct solution?