Question

Make a pair of linear equation if the any case of cyclic quadrilateral are given as angle A =4y+20, angle B = 3y-5
angle C = -4x, angle D = -7x+5​

Answer 1

Answer: For k = 2, the two equations 3x-y+8=0 and 6x-ky=-16 represent coincident lines. Solution: The given equations are 3x-y+8=0 and 6x-ky+16 = 0.

Answer 2

Answer:

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Let the present age of Aftab = x

and present age of his daughter is represented as = y

Seven years ago,

Aftab’s age = x – 7

Age of Aftab’s daughter = y – 7

According to the question,

      (x – 7) = 7 (y – 7 )

=> x – 7 = 7 y – 49

=> x – 7y = – 49 + 7

=> x – 7y = – 42 …           (i)

=> x = 7y – 42

=> Putting y = 5, 6 and 7, we get

=> x = 7 * 5 – 42 = 35 – 42 = – 7

=> x = 7 * 6 – 42 = 42 – 42 = 0

=> x = 7 * 7 – 42 = 49 – 42 = 7

x

-7

0

7

y

5

6

7

 

Three years from now,

Aftab’s age = x + 3

Age of Aftab’s daughter = y + 3

According to the question,

     (x + 3) = 3 (y + 3)

=> x + 3 = 3y + 9

=> x – 3y = 9 – 3

=> x – 3y = 6 …           (ii)

=> x = 3y + 6

=> Putting, y = – 2, –1 and 0, we get

=> x = 3 * (-2) + 6 = – 6 + 6 =0

=> x = 3 * (-1) + 6 = – 3 + 6 = 3

=> x = 3 * 0 + 6 = 0 + 6 = 6    

x

0

3

6

y

-2

-1

0

 

From equation (i) and (ii)

x – 7y = – 42 …           (i)

x – 3y = 6 …                  (ii)

Graphical representation is given as above