plse help me solve this sum

Question

amistre64 · Answer

its a system of equations ....

amistre64 · Answer

you can solve it usually in 3 ways:

substitution, elimination, or matrix math

amistre64 · Answer

since the slopes of each line are not parallel, they will always meet at one point for any value of k

anonymous · Answer

what does it mean that they passes through the same point

amistre64 · Answer

|dw:1369754695254:dw|

amistre64 · Answer

they share a common point, they intersect at a single point ....

amistre64 · Answer

in R^2, if 2 lines are parallel, they never meet.  If the are coincident, they are the same line and share all points in common.

otherwise, they are not parallel and always meet at 1 point.

parallel lines have the same slope ....

anonymous · Answer

but i solve these equations by elimaination, subs...method, 
i can't get the value of k

amistre64 · Answer

9x+5y=k  *4
4x+9y=2  *-9


  36x+20y =  4k
-36x -81y =-18
---------------
        -61y = 4k-18

k = (18-61y)/4
---------------------------------------

9x+5y=k  *9
4x+9y=2  *-5


  81x+45y=9k
-20x-45y =-10
--------------
61x         =9-10k

k = (9-61x)/10

raden · Answer

i sure, the meet point of both line is the solution of that lines.

amistre64 · Answer

equate k with k and you produce a linear solution set with an infinite number of solutions

anonymous · Answer

okay

amistre64 · Answer

k = (18-61y)/4
k = (9-61x)/10

(18-61y)/4 = (9-61x)/10

5(18-61y) = 2(9-61x)

etc ...

amistre64 · Answer

but as i pointed out earlier;  the slopes are not parallel:

-9/5  not equal -4/9,  so they will always meet at one point regardless of the value of k

k = R

anonymous · Answer

@amistre64 
thank u sis

amistre64 · Answer

youre welcome