By equating coefficients of variables, solve the following equations.

i. 3x - 4y = 7; 5x + 2y = 3

ii. 5x + 7y = 17; 3x - 2y = 4

iii. x - 2y = -10; 3x - 5y = -12

iv. 4x + y = 34; x + 4y = 16

(i)

3x - 4y = 7 eq.[1]

5x + 2y = 3 eq.[2]

Multiplying eq.[2] by 2 both side, we get

10x + 4y = 6 eq.[3]

Adding eq.[1] and eq.[3], we get

3x - 4y + 10x + 4y = 7 + 6

⇒ 13x = 13

⇒ x = 1

Putting this in eq.[1], we get

3(1) - 4y = 7

⇒ -4y = 7 - 3

⇒ -4y = 4

⇒ y = -1

(ii)

5x + 7y = 17 eq.[1]

3x - 2y = 4 eq.[2]

Multiplying eq.[1] by 3 both side and Multiplying eq.[2] by 5 both side we get,

15x + 21y = 51 eq.[3]

15x - 10y = 20 eq.[4]

Subtracting eq.[4] from eq.[3], we get

15x + 21y - 15x + 10y = 51 - 20

⇒ 31y = 31

⇒ y = 1

Putting this in eq.[1], we get

5x + 7(1) = 17

⇒ 5x = 10

⇒ x = 2

(iii)

x - 2y = -10 eq.[1]

3x - 5y = -12 eq.[2]

Multiplying eq.[1] by 3

3x - 6y = -30 eq.[3]

Subtracting eq.[2] from eq.[3], we get

3x - 6y - 3x + 5y = -30 + 12

⇒ -y = -18

⇒ y = 18

Putting this in eq.[1], we get

x - 2(18) = -10

⇒ x - 36 = -10

⇒ x = 26

(iv)

4x + y = 34 eq.[1]

x + 4y = 16 eq.[2]

Multiplying eq.[2] by 4 both side, we get

4x + 16y = 64 eq.[3]

Subtracting eq.[3] from eq.[1], we get

4x + 16y - 4x - y = 64 - 34

⇒ 15y = 30

⇒ y = 2

Putting this in eq.[2], we get

x + 4(2) = 16

⇒ x + 8 = 16

⇒ x = 8