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
