Question

(i) If \[\left( \frac{a}{3} + 1, b - \frac{2}{3} \right) = \left( \frac{5}{3}, \frac{1}{3} \right)\] find the values of a and b. 

 

Answer 1

(i)  \[\left( \frac{a}{3} + 1, b - \frac{2}{3} \right) = \left( \frac{5}{3}, \frac{1}{3} \right)\]

By the definition of equality of ordered pairs, we have:

\[\left( \frac{a}{3} + 1, b - \frac{2}{3} \right) = \left( \frac{5}{3}, \frac{1}{3} \right)\]

\[\Rightarrow \left( \frac{a}{3} + 1 \right) = \frac{5}{3} \text{ and } \left( b - \frac{2}{3} \right) = \frac{1}{3}\]
\[ \Rightarrow \frac{a}{3} = \frac{5}{3} - 1 \text{ and } b = \frac{1}{3} + \frac{2}{3}\]
\[ \Rightarrow \frac{a}{3} = \frac{2}{3} \text{ and } b = 1\]
\[ \Rightarrow a = 2\text{  and  } b = 1\]