Question

8. One equation of the pair of dependent linear equation is - 5 x + 7 y = 2. The second equation can
be: (a) 10 x + 14 y + 4 = 0
(b) -10 x - 14 y + 4 = 0 (c)-10 x + 14 y + 4 = 0
(d) 10 - 14 y = - 4
​

Answer 1

Answer:

d is the correct answer for this question

Answer 2

Solution :-

ᴄᴏɴᴄᴇᴘᴛ ᴜsᴇᴅ :-

• A linear equation in two variables represents a straight line in 2D Cartesian plane .

• If we consider two linear equations in two variables, say :-

➻ a1x + b1y + c1 = 0

➻ a2x + b2y + c2 = 0

Then :-

✪ Both the straight lines will coincide if :-

a1/a2 = b1/b2 = c1/c2

➻ In this case , the system will have infinitely many solutions.

➻ If a consistent system has an infinite number of solutions, it is dependent and consistent.

Now, given that, one equation of the pair of dependent linear equation is :-

→ - 5x + 7y = 2

→ - 5x + 7y - 2 = 0

comparing with a1x + b1y + c1 = 0 we get,

• a1 = (-5)
• b1 = 7
• c1 = (-2)

since, the pair of lines are dependent , they will have infinitely many solutions.

then,

→ a1/a2 = b1/b2 = c1/c2

putting a2, b2, c2 values from options now we get,

(a) 10x + 14 y + 4 = 0

→ a2 = 10, b2 = 14 , c2 = 4

So,

→ (-5)/10 = 7/14 = (-2)/4

→ (-1/2) ≠ (1/2) ≠ (-1/2)

therefore, given option is not possible .

(b) -10 x - 14 y + 4 = 0

→ a2 = -10, b2 = -14 , c2 = 4

So,

→ (-5)/(-10) = 7/(-14) = (-2)/4

→ (1/2) ≠ (-1/2) = (-1/2)

therefore, given option is not possible .

(c) -10x + 14 y + 4 = 0

→ a2 = -10, b2 = 14 , c2 = 4

So,

→ (-5)/(-10) = 7/14 = (-2)/4

→ (1/2) = (1/2) ≠ (-1/2)

therefore, given option is not possible .

(d) 10x - 14 y = - 4 => 10x - 14y + 4 = 0

→ a2 = 10, b2 = (-14) , c2 = 4

So,

→ (-5)/10 = 7/(-14) = (-2)/4

→ (-1/2) = (-1/2) = (-1/2)

therefore, given option is correct .

Hence, Option (D) is right answer .

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