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.
(ii) If (x + 1, 1) = (3, y − 2), find the values of x and y.

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:
$\left(\frac{a}{3}+1,b-\frac{2}{3}\right)=\left(\frac{5}{3},\frac{1}{3}\right)$
$$\begin{gathered} \Rightarrow \left(\frac{a}{3}+1\right)=\frac{5}{3}\mathrm{and}\left(b-\frac{2}{3}\right)=\frac{1}{3} \\ \Rightarrow \frac{a}{3}=\frac{5}{3}-1\mathrm{and}b=\frac{1}{3}+\frac{2}{3} \\ \Rightarrow \frac{a}{3}=\frac{2}{3}\mathrm{and}b=1 \\ \Rightarrow a=2\mathrm{and}b=1 \end{gathered}$$

(ii) (x + 1, 1) = (3, y − 2)
By the definition of equality of ordered pairs, we have:
$$\begin{gathered} (x+1)=3\mathrm{and}1=(y-2) \\ \Rightarrow x=2\mathrm{and}y=3 \end{gathered}$$