CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Solve the following systems of equations:

10x+y+2xy=4

15x+y9xy=2

Open in App
Solution

Let 1x+y=t and 1xy=s

Substitute it in given equations, we get

10t+2s=4 ... (1)

15t-9s=-2 ... (2)

Multiplying equation (1) with 3 and equation (2) with 2

30t +6s =12 ... (3)

30t -18s =-4 ... (4)

(4) - (3)

30t-18s-30t-6s=-4-12

-24s =-16

s =1624

s= 23

Substitute s =23 in equation (2)

15t -9(23)=-2

15t -6=-2

15t = -2+6

15t =4

t = 415

We know that

1x+y=t

1x+y= 415

x + y = 154 ... (5)

Also we know that

1xy=s

1xy= 23

x - y = 32 ... (6)

Adding equations (5) and (6)

x+y+x-y=154+32

2x = 15+64

2x = 214

x =218

Substitute x =218 in equation (5)

218+y=154

y = 154-218

y =30218

y = 98

Hence x=218,y=98


flag
Suggest Corrections
thumbs-up
37
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Algebraic Solution
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon