(i) If (a/3 + 1, b – 2/3) = (5/3, 1/3), find the values of a and b.(

1.	(i) If (a/3 + 1, b – 2/3) = (5/3, 1/3), find the values of a and b.(ii) If (x + 1, 1) = (3y, y – 1), find the values of x and y.
Answer» Given as (a/3 + 1, b – 2/3) = (5/3, 1/3) From the definition of equality of ordered pairs, Let us solve for a and b a/3 + 1 = 5/3 and b – 2/3 = 1/3 a/3 = 5/3 – 1 and b = 1/3 + 2/3 a/3 = (5-3)/3 and b = (1+2)/3 a/3 = 2/3 and b = 3/3 a = 2(3)/3 and b = 1 a = 2 and b = 1 ∴ Values of a and b are, a = 2 and b = 1 (ii) Given as (x + 1, 1) = (3y, y – 1) From the definition of equality of ordered pairs, Let us solve for x and y x + 1 = 3y and 1 = y – 1 x = 3y – 1 and y = 1 + 1 x = 3y – 1 and y = 2 Here, y = 2 we can substitute in x = 3y – 1 = 3(2) – 1 = 6 – 1 = 5 Hence, the values of x and y are, x = 5 and y = 2

(i) If (a/3 + 1, b – 2/3) = (5/3, 1/3), find the values of a and b.(ii) If (x + 1, 1) = (3y, y – 1), find the values of x and y.

Answer»

Given as

(a/3 + 1, b – 2/3) = (5/3, 1/3)

From the definition of equality of ordered pairs,

Let us solve for a and b

a/3 + 1 = 5/3 and b – 2/3 = 1/3

a/3 = 5/3 – 1 and b = 1/3 + 2/3

a/3 = (5-3)/3 and b = (1+2)/3

a/3 = 2/3 and b = 3/3

a = 2(3)/3 and b = 1

a = 2 and b = 1

∴ Values of a and b are, a = 2 and b = 1

(ii) Given as

(x + 1, 1) = (3y, y – 1)

From the definition of equality of ordered pairs,

Let us solve for x and y

x + 1 = 3y and 1 = y – 1

x = 3y – 1 and y = 1 + 1

x = 3y – 1 and y = 2

Here, y = 2 we can substitute in

x = 3y – 1

= 3(2) – 1

= 6 – 1

= 5
Hence, the values of x and y are, x = 5 and y = 2

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