**(1) 3a + 5b = 26; a + 5b = 22**

3a + 5b = 26 …… (i)

a + 5b = 22 ……… (ii)

Now by changing the sign of equation (ii) we get

– a – 5b = – 22

Subtracting equation (ii) from (i) we get

2a = 4

a = 4/2

a = 2

Substituting a = 2 in equation (ii) we get

2 + 5b = 22

5b = 22 – 2

5b = 20

b = 20/5

b = 4

∴ solution is (a, b) = (2, 4)

**(2) x + 7y = 10; 3x – 2y = 7**

Given

x + 7y = 10 ……. (i)

x – 2y = 7 ……… (ii)

Multiply equation (i) by 2 and equation (ii) by 7

2x + 14 y = 20

21x – 14 y = 49

Which implies

23 x = 69

x = 69/23

x = 3

Substituting x = 3 in equation (i)

3 + 7y = 10

7y = 10 – 3

7y = 7

y = 7/7

y = 1

∴ Solution is (x, y) = (3, 1)

**(3)** **2x – 3y = 9; 2x + y = 13**

Given

2x – 3y = 9 …… (i)

2x + y = 13 …… (ii)

To subtract equation (ii) from (i)

Change the sign of equation (ii)

2x – 3y = 9

-2x – y = – 13

Which implies

– 4y = – 4

y = 4/4

y = 1

Substituting y = 1 in equation (ii)

2x + 1 = 13

2x = 13 – 12x = 12x = 6

∴ solution is (x, y) = (1, 6)

**(4) 5m – 3n = 19; m – 6n = –7**

Given

5m – 3n = 19 …… (i)

m – 6n = –7 …. (ii)

Multiply equation (ii) by 5

5m – 30n = -35 …. (iii)

Equating (i) and (iii), change the sign of equation (iii)

5m – 3n = 19

– 5m + 30 n = 35

Adding both we get

27n = 54

n = 54/27

⇒ n = 2

Substituting n = 2 in equation (i)

⇒ 5m – 3(2) = 19

⇒ 5m – 6 = 19

⇒ 5m = 25

⇒ m = 5

∴ Solution is (m, n) = (5, 2)

**(5) 5x + 2y = –3; x + 5y = 4**

5x + 2y = – 3 …. (i)

x + 5y = 4 …… (ii)

Multiply equation (i) by 5 and equation (ii) by 2

25 x + 10 y = -15 …. (iii)

2x + 10 y = 8 …. (iv)

Change sign of equation (iv)

25 x + 10 y = -15

– 2x – 10 y = – 8

23 x = -23

x = -1

Substituting x = –1 in equation (ii)

– 1 + 5y = 4

5y = 4 + 1

5y = 5

Y = 1

∴ solution is (x, y) = (–1, 1)

**(6)**

**(7) 99x + 101 y = 499; 101x + 99y = 501**

**Solution:**

**(8) 49x – 57y = 172; 57x – 49y = 252**

**Solution:**