# Find the values of a and b, when:

Question:

Find the values of a and b, when:

(i) $(a+3, b-2)=(5,1)$

(ii) $(a+b, 2 b-3)=(4,-5)$

(iii) $\left(\frac{\mathrm{a}}{3}+1, \mathrm{~b}-\frac{1}{3}\right)=\left(\frac{5}{3}, \frac{2}{3}\right)$

(iv) $(a-2,2 b+1=(b-1, a+2)$

Solution:

Since, the ordered pairs are equal, the corresponding elements are equal.

$\therefore, \mathrm{a}+3=5 \ldots$ (i) and $\mathrm{b}-2=1 \ldots$ (ii)

Solving eq. (i), we get

$a+3=5$

$\Rightarrow a=5-3$

$\Rightarrow a=2$

Solving eq. (ii), we get

$b-2=1$

$\Rightarrow b=1+2$

$\Rightarrow b=3$

Hence, the value of a = 2 and b = 3.

(ii) Since, the ordered pairs are equal, the corresponding elements are equal.

$\therefore, \mathrm{a}+\mathrm{b}=4 \ldots$ (i) and $2 \mathrm{~b}-3=-5 \ldots$ (ii)

Solving eq. (ii), we get

$2 b-3=-5$

$\Rightarrow 2 b=-5+3$

$\Rightarrow 2 b=-2$

$\Rightarrow b=-1$

Putting the value of $b=-1$ in eq. (i), we get

$a+(-1)=4$

$\Rightarrow a-1=4$

$\Rightarrow a=4+1$

$\Rightarrow a=5$

Hence, the value of a = 5 and b = -1.

(iii) Since the ordered pairs are equal, the corresponding elements are equal.

$\therefore \frac{a}{3}+1=\frac{5}{3} \ldots(\mathrm{i})$

$\& b-\frac{1}{3}=\frac{2}{3}$  .......(ii)

Solving Eq. (i), we get

$\frac{a}{3}+1=\frac{5}{3}$

$\Rightarrow \frac{a}{3}=\frac{5}{3}-1$

$\Rightarrow a=3\left(\frac{5}{3}-1\right)$

$\Rightarrow a=5-3$

$\Rightarrow a=2$

Solving eq. (ii), we get

$b-\frac{1}{3}=\frac{2}{3}$

$\Rightarrow b=\frac{2}{3}+\frac{1}{3}$

$\Rightarrow b=\frac{3}{3}$

$\Rightarrow b=1$

Hence, the value of a = 2 and b = 1.

(iv) Since, the ordered pairs are equal, the corresponding elements are equal.

$\therefore, a-2=b-1 \ldots$ (i)

$\& 2 b+1=a+2 \ldots$ (ii)

Solving eq. (i), we get

$a-2=b-1$

$\Rightarrow a-b=-1+2$

$\Rightarrow a-b=1 \ldots$ (iii)

Solving eq. (ii), we get

$2 b+1=a+2$

$\Rightarrow 2 b-a=2-1$

$\Rightarrow-a+2 b=1 \ldots$ (iv)

Adding eq. (iii) and (iv), we get

$a-b+(-a)+2 b=1+1$

$\Rightarrow a-b-a+2 b=2$

$\Rightarrow b=2$

Putting the value of b = 2 in eq. (iii), we get

$a-2=1$

$\Rightarrow a=1+2$

$\Rightarrow a=3$

Hence, the value of a = 3 and b = 2