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

30 miles

step-by-step explanation:

we know that 60 seconds equals 1 minute and 60 minutes 1 hour

44 ft       60 sec     60 min     158400   ft

  *   *   =

1 sec       1 min       1 hour         hour

we know that there are 5280 ft per mile

158400   ft       1 mile         30 miles

  *   =

1   hour               5280 ft     1 hour

so in 1 hour   it can travel 30 miles

the answer is 24

step-by-step explanation: