Solution:

Here,

(4a, 6b) = (8, 12)

Comparing the corresponding first and second components,

or, 4a = 8

or, a = \(\frac{8}{4}\)

or, a = 2

And,

or,6b = 12

or, b = \(\frac{12}{6}\)

or, b = 2

∴ a = 2 and b = 2.

Solution:

Here,

(5m+1,−10) = (16, 3n+2)

Comparing the corresponding first and second cpmponents,

or, 5m + 1 = 16

or, 5m = 16 − 1

or, 5m = 15

or, m = \(\frac{15}{5}\)

or, m = 3

And,

or, 3n + 2 = −10

or, 3n = −10 − 2

or, 3n = −12

or, n = \(\frac{−12}{3}\)

or, n = −4

∴ m = 3 and n = −4.

Solution:

Comparing the coressponding first and second components,

Here,

(2x, 3y) = (−6, 9)

or, 2x = −6

or, x = \(\frac{−6}{2}\)

or, x = −3

And,

or, 3y = 9

or, y = \(\frac{9}{3}\)

or, y = 3

∴ x = −3 and y = 3.

Solution:

Here,

(n− 2, \(\frac{m}{4}\)) = (2, 0)

Comparing the corresponding first and second components,

or, n − 2 = 2

or, n = 2 + 2

or, n = 4

And,

or,\(\frac{m}{4}\) = 0

or, m = 0

∴ n = 4 and m = 0

Solution:

Here,

(35, −5) = (a − 2, b + 3)

Comparing the corresponding value First and second components,

or, a − 2 = 35

or, a = 35 + 2

or, a = 37

And,

or, b + 3 = −5

or, b = −5 − 3

or, b = −8

∴ a = 37 and b = −8

Solution:

Here,

(\(\frac{m}{2}\), 3) = (3, \(\frac{n}{2}\) + 1)

Comparing the corresponding first and second components,

or, \(\frac{m}{2}\) = 3

or, m = 3 × 2

or, m = 6

And,

or, \(\frac{n}{2}\) + 1 = 3

or, \(\frac{n}{2}\) = 3 − 1

or, \(\frac{n}{2}\) = 2

or, n = 2 × 2

or, n = 4

∴ m = 6 and n = 4

Solution:

Here,

(−x, 3) = ( 4, −y)

Comparing the corresponding first and second components,

or, −x = 4

or, x = −4

And,

or, −y = 3

or, y = −3

∴ x = −4 and y = −3

Solution:

Here,

(5x, 7y) = (15, 28)

Comparing thr corresponding first and second components,

or, 5x = 15

or, x = \(\frac{15}{5}\)

or, x = 3

And,

or, 7y = 28

or, y = \(\frac{28}{7}\)

or, y = 4

∴ x = 3 and y = 4

Solution:

Here,

(a − 2, b + 1) = (4, 2b)

Comparing the corresponding first and second components,

or,a − 2 = 4

or, a = 4 + 2

or, a = 6

And,

or, b + 1 = 2b

or, 2b − b = 1

or, b = 1

∴ a = 6 and b = 1

Solution:

Here,

(p + 4, 6) = (10, q)

Comparing the corresponding first and second components,

or, p + 4 = 10

or, p = 10 − 4

or, p = 6

And,

or, q = 6

∴ p = 6 and q = 6

Solution:

Here,

(a + 3, b) = (10, 5)

Comparing the corresponding first and second components,

or, a + 3 = 10

or, a = 10 − 3

or, a = 7

And,

or, b = 5

∴ a = 7 and b = 5

Solution:

Here,

(6,−y) = (−x,−4)

Comparing the corresponding first and second components,

or, −x = 6

or, x = −6

And,

or, −y = −4

or, y = 4

∴ x = −6 and y = 4

Solution:

Here,

(a, 3) = (4, b + 1)

Comparing the corresponding first and second components,

or, a = 4

And,

or, b + 1 = 3

or, b = 3 − 1

or, b = 2

∴ a = 4 and b = 2

Solution:;

Here,

(x, y − 2) = (6, 8)

Comparing the corresponding first and second components,

or, x = 6

And,

or, b − 2 = 8

or, b = 8 + 2

or, b = 10

∴ x = 6 and b = 10

Solution:

Here,

(−p, 6q) = (3, 36)

Comparing the corresponding first and second components,

or,−p = 3

or, p = −3

And,

or, 6q = 36

or, q = \(\frac{36}{6}\)

or, q = 6

∴ p = −3 and q = 6