linear problem: find k so 3x - 2y = 7, kx + 3y = 5 have no
- Thread starter megan0430
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Have you not studied systems of equations at all? (It would be very simple matter to find the value of "k" that creates an inconsistent system, but only if you know what an "inconsistent" system is, is why I ask.)megan0430 said:
Thank you.
Eliz.
Re: linear problem
Hello, megan0430!
If they have no points in common, the two lines are parallel.
. . Parallel lines have the same slope.
\(\displaystyle 3x\,-\,2y\:=\:7\;\;\Rightarrow\;\;y\:=\:\frac{3}{2}x\,+\,\frac{7}{2}\)
. . This line has slope \(\displaystyle \frac{3}{2}\)
\(\displaystyle kx\,+\,3y\:=\:5\;\;\Rightarrow\;\;y\:=\:-\frac{k}{3}\,+\,\frac{5}{3}\)
. . This line has slope -\(\displaystyle \frac{k}{3}\)
If the slopes are equal: \(\displaystyle \,-\frac{k}{3}\:=\:\frac{3}{2}\;\;\Rightarrow\;\;\fbox{k\:=\:-\frac{9}{2}}\)
Hello, megan0430!
If they have no points in common, the two lines are parallel.
. . Parallel lines have the same slope.
\(\displaystyle 3x\,-\,2y\:=\:7\;\;\Rightarrow\;\;y\:=\:\frac{3}{2}x\,+\,\frac{7}{2}\)
. . This line has slope \(\displaystyle \frac{3}{2}\)
\(\displaystyle kx\,+\,3y\:=\:5\;\;\Rightarrow\;\;y\:=\:-\frac{k}{3}\,+\,\frac{5}{3}\)
. . This line has slope -\(\displaystyle \frac{k}{3}\)
If the slopes are equal: \(\displaystyle \,-\frac{k}{3}\:=\:\frac{3}{2}\;\;\Rightarrow\;\;\fbox{k\:=\:-\frac{9}{2}}\)