Which system of equations is inconsistent? a) 2x+8y=6 5x+20y=2 b) 5x+4y=-14 3x+6y=6 c) x+2y=3 4x+6y=5 d) 3x-2y=3 6x-4y=4

Option A and D

Step-by-step explanation:

we know that

A system of equations is inconsistent, when the system has no solutions (because the lines are parallel) and the system is consistent when has at least one solution

Verify each case

case A) we have

2x+8y=6 > equation A

5x+20y=2 > equation B

Multiply the equation A by 2.5 both sides

2.5*(2x+8y)=6*2.5

5x+20y=15 > equation C

Compare equation B and equation C

5x+20y=2 > equation B

5x+20y=15 > equation C

the lines are parallel with different y-intercept

therefore

The system has no solution, hence the system is inconsistent

case B) we have

5x+4y=-14 > equation A

3x+6y=6 > equation B

Multiply equation A by 1.5 both sides

1.5*(5x+4y)=-14*1.5

7.5x+6y=-21 > equation C

Compare equation B and equation C

3x+6y=6 > equation B

7.5x+6y=-21 > equation C

The lines are different (their slopes are not equal)

therefore

The system has only one solution, hence the system is consistent

case C) we have

x+2y=3 > equation A

4x+6y=5 > equation B

Multiply by 3 equation A both sides

3*(x+2y)=3*3

3x+6y=9 > equation C

Compare equation B and equation C

4x+6y=5 > equation B

3x+6y=9 > equation C

The lines are different (their slopes are not equal)

therefore

The system has only one solution, hence the system is consistent

case D) we have

3x-2y=3 > equation A

6x-4y=4 > equation B

Multiply equation A by 2 both sides

2*(3x-2y)=3 *2

6x-4y=6 > equation C

Compare equation B and equation C

6x-4y=4 > equation B

6x-4y=6 > equation C

the lines are parallel with different y-intercept

therefore

The system has no solution, hence the system is inconsistent

answer is d-29

step-by-step explanation:

since you didn't include the picture, i can give you the description so you know how to pick the correct answer. the third quartile of a data is always shown in a box plot. in the middle of your graph should be a box. the third quartile is the value that goes with the far right edge of the box.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)