Advanced Math/Matrices

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Expert: Sherry Wallin - 3/16/2009


Question
y-5x=0
3x-5y=2 is it concident or parallel or intersecting?

Answer

matrix
Ashley~
    What is it you want to know? Are you wanting to know what coincident means, parallel, or intersecting? Or do you want to know how to tell from solving a matrix? Or do you want to know how to work with matrices? I ask this because you can tell immediately (almost) if they are coincident, parallel, or intersecting by putting both into slope-intercept form which I tell my students is 'their best friend'.
y-5x = 0 -> y = 5x  and
3x-5y = 2 -> -5y = -3x + 2 -> y = (3/5)x +-2/5

Notice the slopes are not the same so they are NOT parallel.
Notice they aren't the SAME equation so they are NOT coincident.
Notice they have to be one of those three things so therefore they intersect at just one point, what we call a unique solution to the system.

As far as telling these things from using matrices let's see what occurs. See attached image.

If the lines were parallel you would have gotten 'gibberish' as a final answer something like 2 = 0 and that is NEVER true, i.e there is not values for x and y that make the system true because they are parallel. And if they were coincident you would have lost one of the equations(one of the rows would be 0  0  0 which is ALWAYS true) and any values for x and y would lead to a true statement regardless of which ones you chose.

Sherry Wallin

Expertise

I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

Experience

I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

Education/Credentials
I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

Awards and Honors
Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0

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