# By equating coefficients of variables, solve the following equations.i. 3x - 4y = 7; 5x + 2y = 3ii. 5x + 7y = 17; 3x - 2y = 4iii. x - 2y = -10; 3x - 5y = -12iv. 4x + y = 34; x + 4y = 16

(i)

3x - 4y = 7 eq.

5x + 2y = 3 eq.

Multiplying eq. by 2 both side, we get

10x + 4y = 6 eq.

Adding eq. and eq., we get

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

13x = 13

x = 1

Putting this in eq., we get

3(1) - 4y = 7

-4y = 7 - 3

-4y = 4

y = -1

(ii)

5x + 7y = 17 eq.

3x - 2y = 4 eq.

Multiplying eq. by 3 both side and Multiplying eq. by 5 both side we get,

15x + 21y = 51 eq.

15x - 10y = 20 eq.

Subtracting eq. from eq., we get

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

31y = 31

y = 1

Putting this in eq., we get

5x + 7(1) = 17

5x = 10

x = 2

(iii)

x - 2y = -10 eq.

3x - 5y = -12 eq.

Multiplying eq. by 3

3x - 6y = -30 eq.

Subtracting eq. from eq., we get

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

-y = -18

y = 18

Putting this in eq., we get

x - 2(18) = -10

x - 36 = -10

x = 26

(iv)

4x + y = 34 eq.

x + 4y = 16 eq.

Multiplying eq. by 4 both side, we get

4x + 16y = 64 eq.

Subtracting eq. from eq., we get

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

15y = 30

y = 2

Putting this in eq., we get

x + 4(2) = 16

x + 8 = 16

x = 8

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