Given: . If the coordinates of point A are (8 , 0) and the coordinates of point B are (3 , 7), the y-intercept of is
. If the coordinates of point D are (5 , 5), the equation of line is y =
x +
.

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