Find the values of a and b, when:
(i) (a + 3, b –2) = (5, 1)
(ii) (a + b, 2b – 3) = (4, –5)
(iv) (a – 2, 2b + 1 = (b – 1, a + 2)
Since, the ordered pairs are equal, the corresponding elements are equal.
∴, a + 3 = 5 …(i) and b – 2 = 1 …(ii)
Solving eq. (i), we get
a + 3 = 5
⇒ a = 5 – 3
⇒ a = 2
Solving eq. (ii), we get
b – 2 = 1
⇒ b = 1 + 2
⇒ b = 3
Hence, the value of a = 2 and b = 3.
(ii) Since, the ordered pairs are equal, the corresponding elements are equal.
∴, a + b = 4 …(i) and 2b – 3 = -5 …(ii)
Solving eq. (ii), we get
2b – 3 = -5
⇒ 2b = -5 + 3
⇒ 2b = -2
⇒ b = -1
Putting the value of b = - 1 in eq. (i), we get
a + (-1) = 4
⇒ a – 1 = 4
⇒ a = 4 + 1
⇒ a = 5
Hence, the value of a = 5 and b = -1.
(iii) Since the ordered pairs are equal, the corresponding elements are equal.
…(i)
…(ii)
Solving Eq. (i), we get
⇒ a = 5 – 3
⇒ a = 2
Solving eq. (ii), we get
⇒ b = 1
Hence, the value of a = 2 and b = 1.
(iv) Since, the ordered pairs are equal, the corresponding elements are equal.
∴, a – 2 = b – 1 …(i)
& 2b + 1 = a + 2 …(ii)
Solving eq. (i), we get
a – 2 = b – 1
⇒ a – b = -1 + 2
⇒ a – b = 1 … (iii)
Solving eq. (ii), we get
2b + 1 = a + 2
⇒ 2b – a = 2 – 1
⇒ -a + 2b = 1 …(iv)
Adding eq. (iii) and (iv), we get
a – b + (-a) + 2b = 1 + 1
⇒ a – b – a + 2b = 2
⇒ b = 2
Putting the value of b = 2 in eq. (iii), we get
a – 2 = 1
⇒ a = 1 + 2
⇒ a = 3
Hence, the value of a = 3 and b = 2.