15x+20y+25xy=250 95x+80y+65xy=650?

Question

to solve the equation in givien 1

Answer 1

15x+20y+25xy=250 ---1
95x+80y+65xy=650 ---2


devide eq. 1 and 2 by 5

3x + 4y + 5xy = 50---3
19x + 16y + 13xy = 130 ---4


multiply eq. 3 by 4 and eq. 4 by -1

12x + 16y + 20xy = 200
-19x - 16y - 13xy = -130

some up above 2 equations

-7x + 7xy = 70

devide above equation by -7

x - xy = -10

=> x (1-y) = -10

=> 1 - y = -10/x (where x != 0)

=> -y = -10/x -1

=> -y = (-x - 10)/x

=> y = (x + 10 )/x

put the value of y in equation 3

3x + 4 (x + 10)/x + 5x (x + 10)/x = 50

multiply above equation by x

3x^2 + (4x + 40) + 5x^2 + 50x = 50x

=> 8x^2 + 40 + 4x = 0

=> 8x^2 + 4x + 40 = 0


=> 2x^2 + x + 10 = 0


Now you need to work on to find complex solution for this equation (i.e. value of X is not a real no.)

Hence,

1) There is no solution for this equations in real number range.
2) But you can have complex number solution for this equations


After you find Complex value for x you can substitute that value in equation (1) and will get the values for y

And there will be 2 different combinations of X and Y

Answer 2

the equations are,

15x + 20y + 25xy = 250................(1)
95x + 80y + 65xy = 650................(2)

(1) x 4 gives,

60x + 80y + 100xy = 1000.............(3)

(2) - (3) gives

35x -35xy = -350
or, x -xy = -10..............................(4)

(1) x 19 gives,

285x + 380y + 475xy = 4750.........(5)

(2) x 3 gives,

285x + 240y + 195xy = 1950.........(6)

(5) - (6) gives,

140y + 280 xy = 2800
or, y + 2xy = 20..........................(7)

(4) x 2 gives,

2x - 2xy = -20..............................(8)

(7) + (8) gives,

2x + y = 0
or, y = -2x

putting this value at (8) we get,
2x + 4x^2 = -20
or, 4x^2 + 2x + 20 = 0
or, x^2 + x/2 + 5 = 0

Solve the equation to get the value of x and then substitute it in another equation to find y.

Hope this was helpful.

Answer 3

15x+20y+25xy=250, 15x+20y = -25xy +250 = 25(100-xy)
-------------------=-----, -----------=----------------=---------------
95x+80y+65xy=650, 95x+80y = -65xy +650 = 65(100-xy)

65(15x+20y)= 25(95x+80y), 975x +1300y = 2375x + 2000y
1400x + 700y = 0, 1400x/700 =-y, 2x=-y. You can do the rest.

Answer 4

Solving simultaneous equations is really simple.
Solving them on paper is easier than on a computer, so, I am not doing it now.
Try to reduce the coefficients as much as possible.
Like, divide both equations by 5 to reduce the numbers.
And then try to eliminate unknowns to get equations with only 1 variable.

Answer 5

11x+10y+9xy=90

Answer 6

95x+80y+65xy=650 ............ (1)
15x+20y+25xy=250 ............ (2)

(1)-(2)
80x+60y+40xy=400 ..............(3)
4x+3y+2xy=20 ..............(3/20)....(4)
3x+4y+5xy=50 ..............(2/5) .....(5)
x-y-3xy=-30 ............. (4-5)......(6)
3x-3y-9xy=-90 ............. (6*3)
7x-7xy=-70 ..............
x-xy=-10
y-2xy=-20
2x-2xy=y-2xy
2x=y

Answer 7

It will not take more than 10 minutes. Please solve it yourself. That will boost your confidence in math.