Question

(i) If $(\frac{a}{3}+1,b-\frac{2}{3})=(\frac{5}{3},\frac{1}{3}),$ 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) By the definition of equality of ordered pairs

$(\frac{a}{3}+1,b-\frac{2}{3})=(\frac{5}{3},\frac{1}{3}),$

$\Rightarrow \frac{a}{3}+1=\frac{5}{3}$ and $b-\frac{2}{3}=\frac{1}{3}$

$\Rightarrow \frac{a}{3}=\frac{5}{3}-1$ and $b=\frac{1}{3}+\frac{2}{3}$

$\Rightarrow \frac{a}{3}=\frac{5-3}{3}$ and $b=\frac{1+2}{3}$

$\Rightarrow \frac{a}{3}=\frac{2}{3}$ and $b=\frac{3}{3}$

$\Rightarrow a=2$ and b = 1

(ii) By the definition of equality of ordered pairs

(x + 1, 1) = (3, y - 2)

$\Rightarrow x+1=3$ and 1 = y - 2

$\Rightarrow x=3-1$ and 1 + 2 = y

$\Rightarrow x=2$ and 3 = y

$\Rightarrow x=2$ and y = 3