Question

Choose h and k such that the system has (a) no solution (b) a unique solution or (c) many solutions. Give separate answers for each part. x1 - 3x2 = 1 and 2x1 + hx2 = k

Answer 1

Still trying to get through these review questions from what I missed while ill.

Answer 2

\[x_1-3x_2=1\\
2x_1+hx_2=k\]?

Answer 3

Yep, those are the correct systems. I should have made sure to mention that they were row labels and not exponents. I'm sorry if that was confusing.

Answer 4

i got it

Answer 5

if you pick some random \(h\) and \(k\) there will probably be one unique solution

Answer 6

if you multiply the first equation by 2 you get
\[2x_1-6x_2=2\\
2x_2+hx_2=k\]

Answer 7

if you make \(h=-6\) and \(k=2\) they will be the same line exactly so there will be infinitely many solutions

Answer 8

if you make \(h=-6\) and \(k=\) anything but 2, they will be parallel lines with no intersection

Answer 9

Oh wow! How did you figure that out?

Answer 10

i am the satellite

Answer 11

ok in truth if you wanted to solve it you would have to match up the coefficients to use "elimination"
i just matched up the coefficients of the \(x_1\) term by doubling the first one

Answer 12

Hehehe, that makes sense.

Answer 13

Thank you!