Asked by aayu
Q1. Determine the value of k for which the given system of equations has unique solution:
a) 2x – 3y = 1 ; k x + 5y = 7 b) 4x – 5y = k ; 2x – 3 y = 12
a) 2x – 3y = 1 ; k x + 5y = 7 b) 4x – 5y = k ; 2x – 3 y = 12
Answers
Answered by
Steve
a)
2x-3y = 1
kx+5y = 7
There is no single value of k which determines a unique solution. In fact, since the slope of
2x-3y=1 is 2/3, any value of k which makes the slope of the other line different from 2/3 will work.
So, if -k/5 = 2/3 then k = -10/3 and the line
-10/3 x + 5y = 7
is parallel to the first line.
So, any k different from -10/3 will produce a single solution.
The other pair of lines is even easier. Since it is clear that the lines have different slopes, they must intersect at a single point, regardless of k's value.
2x-3y = 1
kx+5y = 7
There is no single value of k which determines a unique solution. In fact, since the slope of
2x-3y=1 is 2/3, any value of k which makes the slope of the other line different from 2/3 will work.
So, if -k/5 = 2/3 then k = -10/3 and the line
-10/3 x + 5y = 7
is parallel to the first line.
So, any k different from -10/3 will produce a single solution.
The other pair of lines is even easier. Since it is clear that the lines have different slopes, they must intersect at a single point, regardless of k's value.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.