Answer:
z = -12
Step-by-step explanation:
The given system of equations is:
xy/(x + y) = 1 ...........................(1)
xz/(x + z) = 2...........................(2)
yz/(y + z) = 3...........................(3)
From (1): x + y = xy
=> y = xy - x
y = x(y - 1)
x = y/(y - 1).......................................(4)
From (2): 2(x + z) = xz
=> 2x + 2z = xz
2x = xz - 2z
2x = z(x - 2)
z = 2x/(x - 2) ....................................(5)
From (3): 3(y + z) = yz
=> 3y + 3z = yz
3y = yz - 3z
3y = z(y - 3)
z = 3y/(y - 3)....................................(6)
Comparing (5) and (6)
2x/(x - 2) = 3y/(y - 3)
2x(y - 3) = 3y(x - 2)
2xy - 6x = 3xy - 6y
6(y - x) = xy .................................(7)
But from (1): xy = x + y
Using this in (7), we have
6(y - x) = x + y
6y - y - 6x - x = 0
5y - 7x = 0
5y = 7x
x = 5y/7................................................(8)
Using this in (4)
5y/7 = y/(y - 1)
1/(y - 1) = 5/7
(y - 1) = 7/5
y = 1 + 7/5
y = 12/5..........................................(9)
Using this in (8)
x = 5(12/5)/7 = 12/7 .......................(10)
Using (10) in (5)
z = 2x/(x - 2)
z = 2(12/7) ÷ (12/7 - 2)
= 24/7 ÷ -2/7
= 24/7 × (-7/2)
= -24/2 = -12
z = -12.
Answer:
Step-by-step explanation:
Alina=2x---eq(1)
Asim=5x----eq---(2)
So,we get
2x+5x=210
7x=210
x=30
Now,Putting '30' in eq 1 and eq 2
2*30=60
5*30=150
Therefore Alina got 60 Rs while Asim got 150 Rs
Sounds to me as tho you are to graph 3x+5y<10, and that after doing so you are to restrict the shaded answer area created by the "constraint" inequality x≤y+1. OR x-1 ≤ y OR y≥x-1. If this is the correct assumption, then please finish the last part of y our problem statement by typing {x-y<=1}.
First graph 3x+5y = 10, using a dashed line instead of a solid line.
x-intercept will be 10/3 and y-intercept will be 2. Now, because of the < symbol, shade the coordinate plane BELOW this dashed line.
Next, graph y=x-1. y-intercept is -1 and x intercept is 1. Shade the graph area ABOVE this solid line.
The 2 lines intersect at (1.875, 0.875). To the LEFT of this point is a wedge-shaped area bounded by the 2 lines mentioned. That wedge-shaped area is the solution set for this problem.
Answer: 983.33
Step-by-step explanation:
(0.5+0.5) x 983.33
1 x 983.33 = 983.33
