Answer:
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
<em><u>Verify each case</u></em>
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
