solving a 2x2 system of linear equations that is inconsistent or...

Question

Two systems of equations are given below.

For each system, choose the best description of its solution.

If applicable, give the solution.

-3x + y = -9

3x-y-9=0

The system has no solution.

The system has a unique solution: (x,y) = (,)

The system has infinitely many solutions.

They must satisfy the following equation: y=

-2x+y=-6

2x-y=-6

The system has no solution.

The system has a unique solution: (x,y) = ( , )

The system has infinitely many solutions.

They must satisfy the following equation:y=

Answer 1

Hi James,

We begin each problem by solving it using the elimination technique, and see what results.

In the first problem, adding the two equations together gives -9 = -9, since the x’s and y’s cancel out due to their opposite signs. That means the system has infinitely many solutions, as long as they satisfy the equation y = 3x - 9. This equation was found by rearranging the first equation originally given in the problem.

In the second problem, adding the two equations together gives 0 = -12. Since that is a false statement, the system has no solution.

Please let me know if I can be more helpful, thanks!

Joe