Question

2. Solve the following simultaneous equations
(1) 3a + 5b = 26; a + 5b = 22
(3) 2x - 3y = 9; 2x + y = 13
(5) 5x + 2y = -3; x + 5y = 4
(7) 99x + 101y = 499; 101x + 994 = 501
(8) 49x - 57y = 172; 57x - 49y = 252​

Answer 1

3a+5b=26

a+5b=22

on subtraction signs will change

3a+5b=26

-a-5b=-22

2a=4

a=4/2

a=2

now substituting a=2 in equation 1

3×2+5b=26

6+5b=26

5b=26-6=20

b=20/5

b=4

so a=2 and b=4

2x = 9+3y

x = 9+3y/2

then putting the value of x in 2nd equation

2x+y = 13

2×9+3y/2 + y = 13

9+3y+y = 13

9+4y = 13

4y = 13 - 9

4y = 4

y = 4/4

y = 1

now in equation 2nd

2x + y = 13

now putting y=1

2x + 1 = 13

2x = 13 - 1

2x = 12

x = 12/2

x = 6

consider 99x+101y=499

            101x+99y=501

multiplying equation (1) by -101 we get

-9999x-10201y=-50,399

multiplying equation (2) by 99

9999x+9801y=49,599

adding (3) and (4) we get

-400y=-800

y=2

substituting y=2 in equation (1) we get

99x+202=499

99x=499-202

99x=297

x=297/99

x=3

check

99(3)+101(2)=297+202=499

Given :-

49x - 57y = 172 and

57x-49y=252

Adding (i) and (ii), we get

106x - 106y = 424

=> x - y = 4

Now substracting (i) and (ii), we get

-8x - 8y = -80

=> x + y = 10

Adding (iii) and (iv), we get

2x = 14

=> x = 7

putting the value of x in question (iii), we get

y = 3

I hope it will help you