Question

choose h and k such that the system has (a) no solutions, (b) a unique solution and (c) many solutions.
1 -3 1
2 h k

Answer 1

Tech your question seems like it is lacking something. I can't do anything with this :(

Answer 2

i made it to matrix form

Answer 3

original equations are
x1-3x2=1
2x1+hx2=k

Answer 4

Oh that is a matrix?

Answer 5

yes

Answer 6

ok.

\[x-3y=1\]
\[2x+hy=k\]
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if we want no solution we want the lines to be parallel.
So we want the same slope.
\[y=\frac{1}{3}x-\frac{1}{3}\]
\[y=\frac{-2x}{h}+\frac{k}{h}\]
So we want 1/3=-2/h <-------solve for h
and this will give you the h so that the two lines that never cross.
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now we want there to be infinity many solutions which means we want the lines to lay on top of each other
so we want same slope and same y-intercept
so we have 1/3=-2/h and -1/3=k/h <---solve these two equations

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Answer 7

now for one solution that means we want different slope with any y-intercept

so we want \[\frac{1}{3} \neq \frac{-2}{h}\]