Question

Solve : 97x + 103 y = 497 ; 103.x + 97y - 503
Solution :
103x + 97y = 503 .... (1)
+ 97x + 103y = 497 .... (II)
200x + 200y = .... Adding (1) and (IT)
Dividing by 200, we get
x + y =
103x + 97y = 503 ..
-97x + 103y = -497 ... (II)
- 6 = 6 .... by subtracting (II) fr
Dividing the equation by 6, we get
x - y = o... (IV)
By solving equations (III) and (IV) we get,
x= f:y= f​

Answer 1

Let 97x+103y=497.....(1)

And 103x+97y=503....(2)

Now by double addition subtraction

Adding eq. (1) &(2)

97x +103y = 497.....(1)

+

103x+97y = 503.....(2)

200x +200y =1000

Now dividing throughout by 200

We ge x+y=2..... (3)

Now subtracting eq.(1) &(2)

97x+103y = 497

-

103x+97y =503

-6x + 6y = -6

Dividing throughout by 6

We get -x +y = -1..... (4)

Now adding eq. (3) &(4)

X+Y = 2

+

-X+Y = -1

X get cancelled because of opposite signs

2y=1

Y=1/2

Now resubstituting the value of Y = 1 in eq. (3)

Since X + Y = 2

X+1/2 = 2

X =2+2/1

X =4

THEREFORE THE ANSWER IS (4,1/2).

Answer 2

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