Which system of equations is inconsistent?

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mayatrepp mayatrepp

06-03-2017
Mathematics

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Which system of equations is inconsistent?

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OrethaWilkison OrethaWilkison · Answer 1 · 2018-11-20T13:20:13+01:00

Answer:

Option A is correct.

The system of equation is inconsistent is;

2x+8y=6

5x+20y=2

Explanation:

* A system of equations is called an inconsistent system, if there is no solution because the lines are parallel.

* If a system has at least one solution, it is said to be consistent .

*A dependent system of equations is when the same line is written in two different forms so that there are infinite solutions.

(A)

2x+8y=6

5x+20y=2

This is inconsistent, because as shown below in the graph of figure 1 that the lines do not intersect, so the graphs are parallel and there is no solution.

(B)

5x+4y=-14

3x+6y=6

this system of equation is Consistent because it has exactly one solution as shown below in the graph of Figure 2 and also it is independent.

(C)

x+2y=3

4x+6y=5

this system of equation is Consistent because it has exactly one solution as shown below in the graph of Figure 3.

(D)

3x-2y=2

6x-4y=4

this is a consistent system and has an infinite number of solutions, it is dependent because both equations represent the same line. as shown below in the graph of Figure-4.

Therefore, the only Option A system of equation is inconsistent.

nishantwork777 nishantwork777 · Answer 2 · 2021-10-19T12:20:54+02:00

The system of equation which is inconsistent is:

(A)

[tex]2x+8y=6\\5x+20y=2[/tex]

As, the graph(11) shows , the lines do not intersect , the system is inconsistent.

Step-by-step explanation:

Given information:

Equations are given:

We know that ,

A system of equation is called inconsistent system, is the lines are parallel and there is no solution.

If there is at least a solution the system of equation is consistence.

(A)

[tex]2x+8y=6\\5x+20y=2[/tex]

As, the graph(11) shows , the lines do not intersect , the system is inconsistent.

(B)

[tex]5x+4y=14\\3x+6y=6[/tex]

As, the graph(22) shows the system of equation is having a solution hence the system of equation is consistent.

(C)

[tex]x+2y=3\\4x+6y=5[/tex]

There is exactly one solution is given by the graph(33) hence the system of equation is consistent.

(D)

[tex]3x-2y=2\\6x-4y=4[/tex]

The lines in the graph (44) are overlapping hence the system is having infinite number of solution. The system of equation is consistent.

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