Question

If the ordered pairs (a, -1) and (5,



b.belong to {(x, y) : y = 2x - 3}, find the values of a and b

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{(a,-1)\;and\;(5,b)\;belong\;to\;\{(x,y):\;y=2x-3\}}$

$\underline{\textbf{To find:}}$

$\textsf{The values of a and b}$

$\underline{\textbf{Solution:}}$

$\mathsf{Since\;(a,-1)\;and\;(5,b)\;belong\;to\;\{(x,y):\;y=2x-3\},}$

$\mathsf{we\;have}$

$\mathsf{-1=2a-3}\;\;\;\;\;\&\;\;\;\;\mathsf{b=2(5)-3}$

$\mathsf{-1+3=2a}\;\;\;\;\;\&\;\;\;\;\mathsf{b=10-3}$

$\mathsf{2a=2}\;\;\;\;\;\&\;\;\;\;\mathsf{b=7}$

$\mathsf{a=1}\;\;\;\;\;\&\;\;\;\;\mathsf{b=7}$

$\underline{\textbf{Answer:}}$

$\textbf{a=1 and b=7}$

$\underline{\textbf{Find more:}}$

If U={x:x in N x<=30} A={x:x is prime <5} B={x:x is a perfect square <=10} and C={x:x is a perfect cube <=30} then verify the following results : (i) (A uu B)'=A'nn B' (ii)(A nn B)'=A'uu B' (iii) (A nn B)nn C=A nn(B nn C) (iv) A'-B'=B-A

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Answer 2

The values of a = 1 & b = 7

Given :

The ordered pairs (a, -1) and (5,b) belong to {(x, y) : y = 2x - 3}

To find :

The value of a and b

Solution :

Solution :Step 1 of 3 :

Form the equations

Here the given set is

{(x, y) : y = 2x - 3}

Now it is given that the ordered pairs (a, -1) and (5,b) belong to {(x, y) : y = 2x - 3}

Thus we get

- 1 = 2a - 3 - - - - - (1)

b = ( 2 × 5 ) - 3 - - - - - (2)

Step 2 of 3 :

Find the value of a

From Equation 1 we get

- 1 = 2a - 3

⇒ 2a - 3 = - 1

⇒ 2a = 2

⇒ a = 1

The value of a = 1

Step 3 of 3 :

Find the value of b

From Equation 2 we get

b = ( 2 × 5 ) - 3

⇒ b = 10 - 3

⇒ b = 7

The value of b = 7

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