Question

Given that (2,1) is one of the solution of simultaneous equations 3x+py=4 and x^2+ky+2x=11 where p and k are constants.Find the value of k,of p and the other solution.

Answer 1

I found p=-2 and k=3

Answer 2

@Kainui

Answer 3

(2,1) is one of the solution but i don't know how to find the other solution

Answer 4

Any idea?

Answer 5

@Kainui

Answer 6

value of p can be obtained by substituting x,y as 2,1 in the linear equation.

Answer 7

and k can be obtained by putting x=2 in the quadratic equation, then the quadratic can be solved so other root will also be known.

Answer 8

ya,i found already for value of p and k

Answer 9

p=-2 and k=3

Answer 10

but i don't know how to find the other solution

Answer 11

@ganeshie8

Answer 12

p = -2
k = 3

are right! good job :)
lets find the other solution

Answer 13

should we insert p=-2 and k=3 into the equation?

Answer 14

thats a good idea, so the given equations ` 3x+py=4 and x^2+ky+2x=11 ` become :
\[3x-2y = 4\\x^2+3y+2x=11\]

Answer 15

\[x=\frac{ 2y+4 }{ 3 }\]

Answer 16

may be isolate \(y\) instead

Answer 17

okay

Answer 18

so that substitution becomes simple

Answer 19

\[-2y=4-3x\]\[y=-\frac{ 4-3x }{ 2 }\]\[y=\frac{ 3x-4 }{ 2 }\]

Answer 20

looks good, plug that in second equation

Answer 21

alright

Answer 22

\[x^2+3(\frac{ 3x-4 }{ 2 })+2x=11\]

Answer 23

\[x^2+\frac{ 9x-12 }{ 2 }+2x=11\]

Answer 24

\[\frac{ 2x^2 }{ 2 }+\frac{ 9x-12 }{ 2 }+\frac{ 4x }{ 2 }=11\]

Answer 25

\[2x^2+13x-12=22\]

Answer 26

\[2x^2+13x-34=0\]

Answer 27

do u remember this ?

product of roots = c/a ?

Answer 28

-34/2

Answer 29

-17

Answer 30

yes that product of roots has to eqal -34/2

Answer 31

\[\alpha \beta = -17\]

Answer 32

and we know that one root is \(2\)

Answer 33

so :

\[2 \beta = -17\]

Answer 34

\[ \beta = -\dfrac{17}{2}\]

Answer 35

so the x value of solution is \(\large x = -\dfrac{17}{2}\)

Answer 36

plug this in first equation and solve \(y\)

Answer 37

\[y=\frac{ 3x-4 }{ 2 }\]\[y=\frac{ 3(-\frac{ 17 }{ 2 })-4 }{ 2 }\]\[y=-\frac{ 59 }{ 4 }\]

Answer 38

Thnx @ganeshie8

Answer 39

yw:)

Answer 40

that looks perfect!

Answer 41

Thnx :)