Question

Which system of equations is inconsistent?

Answer 1

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.

Answer 2

The system of equation is inconsistent is $\left\{ \begin{aligned}2x + 8y &= 6 \hfill\\5x + 20y &= 2 \hfill\\\end{aligned} \right..$ Option (a) is correct.

Further explanation:

Consider ${a_1}x + {b_1}y + {c_1}$ and ${a_2}x + {b_2}y + {c_2}.$

If $\dfrac{{{a_1}}}{{{a_2}}} \ne \dfrac{{{b_1}}}{{{b_2}}}$ then the system of equation has exactly one solution and the system of equations are consistent.

If $\dfrac{{{a_1}}}{{{a_2}}} = \dfrac{{{b_1}}}{{{b_2}}} = \dfrac{{{c_1}}}{{{c_2}}}$ then the system of equation has infinite many solution and the system of equations are consistent.

If $\dfrac{{{a_1}}}{{{a_2}}} = \dfrac{{{b_1}}}{{{b_2}}} \ne \dfrac{{{c_1}}}{{{c_2}}}$ then the system of equation has no solution and the system of equations are inconsistent.

Explanation:

In option (a),

$\dfrac{2}{5} = \dfrac{8}{{20}} \ne \dfrac{6}{2}$

Hence, system of equations is inconsistent.

Therefore, option (a) is correct.

In option (b),

$\dfrac{5}{3} \ne \dfrac{4}{6}$

Hence, system of equations is consistent.

Therefore, option (b) is not correct.

In option (c),

$\dfrac{1}{4} \ne \dfrac{2}{6}$

Hence, system of equations is consistent.

Therefore, option (c) is not correct.

In option (d),

$\dfrac{3}{6}&=\dfrac{{ - 2}}{{ - 4}}&=\dfrac{2}{4}$

Hence, system of equations is consistent.

Therefore, option (d) is not correct.

The system of equation is inconsistent is $\left\{ \begin{aligned}2x + 8y= 6\hfill\\5x + 20y = 2 \hfill\\\end{aligned}\right..$ Option (a) is correct.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Lines

Keywords: consistent, inconsistent, equations, system of equations, parallel lines, intersecting lines, coincident lines, no solution, many solution, one solution.