Question

please complete the table and help me

Answer 1

Answer:

1.)

eqn 1 =2x-3y-8 = 0 [ a1 = 2 , b1 = -3 , c1 = -8]

eqn 2 = 4x - 6y - 9 = 0 [ a2 = 4 , b2 = -6 , c2 = -9 ]

a1/a2 = 2/4 = 1/2

b1/b2 = -3/-6 = 1/2

c1/c2 = -8/-9 = 8/9

a1/a2 = b1/b2 ≠ c1/c2

it is inconsistent solution , no solution & parallel lines

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2.)

eqn 1 = x - 2y = 0 [ a1 = 1 , b1 = -2 , c1 = 0 ]

eqn 2 = 3x + 4y - 20 = 0 [ a2 = 3 , b2 = 4 , c2 = -20 ]

a1/a2 = 1/3

b1/b2 = -2/4 = -1/2

c1/c2 = 0/-20 = 0

a1/a2 ≠ b1/b2 ≠ c1/c2

it is consistent solution , unique solution & intersecting lines

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3.) NOTE - REARANGE EQN IN FORM OF ax + by + c

eqn 1 = x +y - 6 [ a1 = 1 , b1 = 1 , c1 = -6 ]

eqn 2 = 2x +2y - 12 = 0 [ a2 = 2 , b2 = 2 , c2 = -12 ]

a1/a2 = 1/2

b1/b2 = 1/2

c1/c2 = -6/-12 = 1/2

a1/a2 = b1/b2 = c1/c2

It is consistent solution , infinitely many solution & coincident lines.

Step-by-step explanation:

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