Latest Maths Olympiad Aptitude Question SOLUTION: Q. THE NUMBER OF VALUES OF k FOR WHICH THE SYSTEM OF EQUATIONS x + y = 2 kx + y = 4 x + ky = 5 HAS ATLEAST ONE SOLUTION IS

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Q. THE NUMBER OF VALUES OF k FOR WHICH THE SYSTEM OF EQUATIONS
x + y = 2
kx + y = 4
x + ky = 5
HAS ATLEAST ONE SOLUTION IS

Asked In Maths Olympiad NAVEEN GUPTA (11 years ago)

Solved FAISAL RIZWAN Read Solution (7)

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Read Solution (7) :

Garima  (11 years ago)

one value of k=3.5=7/2
x=4/5
y=6/5

Is this solution Helpfull? Yes (5) | No (2)  

FAISAL RIZWAN  (10 years ago)

x + y = 2 equation (1)
kx + y = 4 equation (2)
x + ky = 5 equation (3)

soln:-substitute the value of x from eqn 1 to eqn 2
k(2-y)+4 equation (4)
5-ky+y=2 from eqn 3
---------
2k-5=2
k=7/2

Nowput the value of k in eqn 3 and substitute the value of x from eqn 1
(2-y)+7/2y=5
on solving we get
y=6/5

Now put the value of y in eqn 1 then in solving we get x=4/5
So,x=4/5,y=6/5and k=7/2

Is this solution Helpfull? Yes (2) | No   

varun singh  (11 years ago)

two values of x are 3.5 and 1

Is this solution Helpfull? Yes (1) | No   

varun singh  (11 years ago)

two value of k= 3.5 and 1

Is this solution Helpfull? Yes (1) | No   

Rakesh  (11 years ago)

@garima.. I think ur solution is wrong
x=2-y
k(2-y)+y=4 i.e y=2k-4 when we put this in 3rd equation we get
2k^2-6k+6=5

which has 2 real values one approx .5 and one approx 3.5

Is this solution Helpfull? Yes | No (3)  

saiharshavellanki  (10 years ago)

given
x+y=2 =>x=2-y
put the values of x in remaining 2 equations . then we get following equation
y=(4-2k)/(1-k) . and y=3/(k-1) .
equating values of y
3/(k-1)=(4-2k)/(1-k)
=>2k^2 -9k+7 =o
=>k=(9+5)/4 , (9-5)/4
=>k=3.5,1
=>there are 2 values of k.

Is this solution Helpfull? Yes | No   

saiharshavellanki  (10 years ago)

given
x+y=2 =>x=2-y
put the values of x in remaining 2 equations . then we get following equation
y=(4-2k)/(1-k) . and y=3/(k-1) .
equating values of y
3/(k-1)=(4-2k)/(1-k)
=>2k^2 -9k+7 =o
=>k=(9+5)/4 , (9-5)/4
=>k=3.5,1
=>there are 2 values of k.
but on substituting,we get solution only when k=3.5

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