Question

solve the following pairs of equations by reducing them to a pair of linear equations


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Answer 1

1/3x+y + 1/3x - y = 3/4...(1)

1/2(3x + y) - 1/ 2(3x - y) = -1/8 ..(2)

substitute the value 1/3x+y = m and 1/3x-y= n

m+n= 3/4 ...(3)

multiply equation with 4,

4m+4n= 3

2m + 2n = -1/8

multiply equation with 8,

16m - 16n=-1 ....(4)

multiply equation (3) with 4,

16m + 16n = 3 ...(5)

adding equation (5) and (4),

16m + 16n = 3

16m - 16n = -1

+ + +

—————————-—

32m = 2

m = 1/ 16

substitute m= 1/16 in equation (3),

m + n = 3/4

1/16 + n = 3/4

n = 3/4 - 1/16

n = 12/16 - 1/16

n = 11/16

resubstituting the value m= 1/3x+y and n= 1/3x-y,

m= 1/3x+y and n= 1/3x-y

1/16 = 1/3x+y and 11/16 = 1/3x-y

3x+y = 16 ...(6) and 16/11 = 3x-y

and 16 = 33x-11y ...(7)

multiplying equation (6) with 11 ,

33x+11y = 176 .....(8)

adding equation (8) and (7),

33x+11y = 176

33x-11y = 16

+ + +

——————-------------

66x = 192

x = 192/ 66

x = 32/11

substitute x = 32/11 in equation (6),

3x + y =16

3(32/11) + y = 16

y= 180

Answer 2

Answer:

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