SOLUTION: PLEASE HELP ME! please! x + 6y = 196 689 = (6201/230)y + (4823/460)x A Vertical BHorizontal CHorizon DNot Parallel and Not Perpendicular E Parallel F Perp

Algebra ->  College  -> Linear Algebra -> SOLUTION: PLEASE HELP ME! please! x + 6y = 196 689 = (6201/230)y + (4823/460)x A Vertical BHorizontal CHorizon DNot Parallel and Not Perpendicular E Parallel F Perp      Log On


   

Question 768532: PLEASE HELP ME! please!

x + 6y = 196
689 = (6201/230)y + (4823/460)x
A Vertical
BHorizontal
CHorizon
DNot Parallel and Not Perpendicular
E Parallel
F Perpendicular

-2y = -380 + 14x
y = -7x + 190
A Horror
BHorizontal
CHorizon
DPerpendicular
E Parallel
F Not Parallel and Not Perpendicular
5x + 4y = -60
y = (-4/5)x - (3/5)
A Vertical
BVertigo
CVercengeterix
DPerpendicular
E Parallel
F Not Parallel and Not Perpendicular
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
system%28x+%2B+6y+=+196%2C689+=+%286201%2F230%29y+%2B+%284823%2F460%29x%29 is a system of linear equations.
x+%2B+6y+=+196 is the equation of a line, and
689+=+%286201%2F230%29y+%2B+%284823%2F460%29x is the equation of another line.
Neither one of those lines is horizontal, because horizontal lines have equations that say
y=somenumber.
Neither one of those lines is vertical, because vertical lines have equations that say
x=somenumber
The lines are slanted with some slope.
The slope of a line is how much the y increases/rises for each unit x gains/runs. It is a ratio.
A way of figuring the slope from the equation is to "solve for y".
x+%2B+6y+=+196 --> 6y+=+x%2B196 --> y+=+x%2F6%2B196%2F6 --> y+=+%281%2F6%29x%2B196%2F6
Each time x increases by 1, y increases by 1%2F6.
The slope of x+%2B+6y+=+196 is 1%2F6
The equation 689=%286201%2F230%29y%2B%284823%2F460%29x looks complicated, but it could simplify to something like x+%2B+6y+=+196
460=230%2A2, , and multiplying both sides times 460=230%2A2, the equation gets simplified.
689=%286201%2F230%29y%2B%284823%2F460%29x --> 1=%289%2F230%29y%2B%287%2F460%29x --> 1%2A460=2%2A230%2A%289%2F230%29y%2B460%284823%2F460%29x --> 460=18y%2B7x
Solving for y we can figure out the slope of that line
460=18y%2B7x --> -7x%2B460=18y --> y=%28-7%2F18%29x%2B460%2F18
The slope is -7%2F18.
If the two lines had the same slope, they would be parallel, or would be exactly the same line.
If they were the same line, all points in one line would also belong to the other line, and the coordinates of all the infinite points in the line would be solutions to the system.
If the lines were parallel, they would not intersect, and the system of equation would not have a solution.
These two lines intersect at some point, and the coordinates of that point are the solution of the system.
If the two lines were perpendicular, the product of their slopes would be -1.
%281%2F6%29%28-18%2F7%29=-3%2F7%3C%3E-1 so the lines are not perpendicular.
The answer is highlight%28D%29 _ Not Parallel and Not Perpendicular.

system%28-2y+=+-380+%2B+14x%2Cy+=+-7x+%2B+190%29
-2y+=+-380+%2B+14x --> -2y%2F%28-2%29=-380%2F%28-2%29%2B14x%28-2%29 --> y=+190+-7x --> y=+-7x%2B190
In this case twe two equations represent the same line.
Neither equation is y=somenumber, so neither line is horizontal.
Beyond that, I have no idea what answer your teacher expects.
Horror?
Would your teacher say that a line is parallel to itself?
I would say that highlight%28F%29 (Not Parallel and Not Perpendicular) is correct, because I consider two lines that are the same line not to be parallel lines.

system%285x+%2B+4y+=+-60+%2Cy+=+%28-4%2F5%29x+-+%283%2F5%29+%29
5x+%2B+4y+=+-60 --> 4y+=-5x+-60 --> y+=-5x%2F4+-60%2F4 --> y+=%28-5%2F4%29x+-15
The slope of that line is -5%2F4.
The slope of y+=+%28-4%2F5%29x+-+%283%2F5%29 is -4%2F5.
They are not the same slope, so the lines are not parallel.
%28-5%2F4%29%28-4%2F5%29=1%3C%3E-1, so the lines are not perpendicular.
Neither equation is x=somenumber, so neither line is vertical.
I would again say that highlight%28F%29 (Not Parallel and Not Perpendicular) is correct.