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# Choosethe best description of the system

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

select all that apply:
inconsistent
independent
dependent
consistent

### 2 Answers by Expert Tutors

Carol H. | Experienced Mathematics Tutor w/ Master's Degree in MathExperienced Mathematics Tutor w/ Master'...
4.9 4.9 (272 lesson ratings) (272)
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.

Michael F. | Mathematics TutorMathematics Tutor
4.7 4.7 (6 lesson ratings) (6)
0
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.