Choosethe best description of the system

Question

4x-3y=10

-20x+15y=50

 

select all that apply:

inconsistent

independent

dependent

consistent

Answer 1

5(4x -3y) = 10(5)      -20x + 15y = 50

20x - 15y = 50           20x - 15y  = 50

                                             0 = 100

 

An independent system has a unique solution.

A dependent system has no unique solution.

An inconsistent system is a system that has no solution.

 

This system would be inconsistent because 0 does not equal 100, which shows there is no solution. The lines would be parallel.

 

Another approach would have been to find the slopes of both lines to find out that they are equal.

4x - 3y = 10                  20x - 15y = 50

     -3y = -4x + 10                 -15y = -20x + 50

        y = 4/3 x + 10/3                    y = 20/15 x + 50

                                                     y - 4/3 x + 50

 

Since both lines have a slope = 4/3. the lines are parallel and inconsistent.

 

 

 

 

 

 

 

 

Answer 2

4x-3y=10
-20x+15y=50

The second equation divided by -5 gives

4x-3y=-10

These are two parallel lines.  The equation has no solution.  The equations are inconsistent.