Question

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Convert the following equations into simultaneous equations and
solve:√x/y=4, 1/X+1/y=1/xy ​

Answer 1

Given:

√x/y=4

1/x+1/y=1/xy ​

To Find:

Simultaneous equations and solution of the above expression.

Solution:

1) The above equations are not in the form of the correct general notation form of the equation which is ax + by = c.

2) first equation is :

• √x/y = 4

• x/y = 4²

• x/y = 16

• x = 16y

• x - 16y = 0   ---------------- (i)

3) Now the second equation is:

• 1/x + 1/y = 1/xy

• (x+y)/xy = 1/xy

• x+y = 1      ---------------- (ii)

4) Now subtract the equation (i) and (ii)

•    x - 16y = 0

          - x -   y   =- 1

          0x -17y  = -1

•   y = 1/17

5) Now substitute the value of y in any of the equation

• x + y = 1

• x + 1/17 = 1

• x = 1 - 1/17

• x = 16/17

Simultaneous equations are x - 16y = 0, x + y =1.

Values are x = 1/17, y = 16/17.