Question

find the solutions of pair of equations CA by X + 8 by Y is equal to -1 and 1 by X - 2 by Y is equal to 2​

Answer 1

Solution:

Given system of equations:

x+8/y = -1

=> x = -1-8/y

=> x = (-y-8)/y ---(1)

and

1/x-2/y = 2

=> 1/x = 2+2/y

=> 1/[(-y-8)/y] = 2+2/y

/*from(1)*/

=> y/(-y-8) = (2y+2)/y

Do the cross multiplication, we get

=> y² = (-y-8)(2y+2)

=> y² = -2y²-2y-16y-16

=> y²+2y²+2y+16y+16=0

=> 3y²+18y+16=0

Splitting the middle term, we get

=> 3y²+12y+4y+16 =0

=> 3y(y+4)+4(y+4)=0

=> (y+4)(3y+4)=0

=> y+4 = 0 or 3y+4 = 0

=> y = -4 or y = -4/3

Substitute y values in equation (1), we get

case I :

if y = -4

x = (-y-8)/y

= [-(-4)-8]/(-4)

= (4-8)/(-4)

= (-4)/(-4)

= 1

x = 1 , y = -4

case II :

if y = -4/3

x = [-(-4/3)-8]/(-4/3)

= [4/3-8]/(-4/3)

= [(4-24)/3]/(-4/3)

= (-20)/(-4)

= 5

Therefore,

x = 5, y = -4/3

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