Question

4. The system of equations 3x – 6y = 20 and 2x – 4y = 3 is

A. dependent.
B. independent.
C. consistent.
D. inconsistent.

Answer 1

3x - 6y = 20
-6y = -3x + 20
y = 1/2x - 20/6.....slope = 1/2...y int = -20/6 = -10/3

2x - 4y = 3
-4y = -2x + 3
y = 1/2x - 3/4..slope = 1/2...y int = -3/4

same slope, different y int = parallel lines = no solution = inconsistent

Answer 2

The correct option is D.

Explanation:

The given system of equations is

`3x-6y=20`

`2x-4y=3`

If a system of equations has no solution, then the system of equations is inconsistent.

If a system of equations has solutions, then the system of equations is consistent.

(a) If the system has one solution, then it is independent.

(b) If the system has infinitely many solutions, then it is dependent.

If two lines are
`ax_1+by_1+c_2=0\text{ and }ax_2+by_2+c_2=0` and

`(a_1)/(a_2)=(b_1)/(b_2)\\eq (c_1)/(c_2)`

then the system of equations is inconsistent.

`(a_1)/(a_2)=(3)/(2)`

`(b_1)/(b_2)=(-6)/(-4)=(3)/(2)`

`(c_1)/(c_2)=(-20)/(-3)=(20)/(3)`

Since
`(a_1)/(a_2)=(b_1)/(b_2)\\eq (c_1)/(c_2)`, therefore the given system of equation is inconsistent.

Hence, the correct option is D.