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Mathematics
OpenStudy (anonymous):

I'm trying to find the linear equation for this: -2x + y = 5 4x -2y = 9 I think it's undefined. Help?

OpenStudy (anonymous):

Yes - you're correct because solving for your system of equations yields a nonsense answer. Let's go through your solution steps. 1) Double every term in the first equation. (Note: this doesn't change the equation because your multiplying both sides proportionally.) 2) Add both sides "straight down" of equations one and two. 3) Notice that all the terms cancel on the left but the right side is 19 --> 0=19 which is impossible! 4) The net effect is that these lines do not have any single point (ie a solution that satisfies both equations) in common. Can you prove why these lines do not cross each other on the graph plane?

OpenStudy (anonymous):

Oh, I see! I'm afraid I don't know how to prove it though. I'm sorry, I'm usually pretty intelligent, but when it comes to math...

OpenStudy (anonymous):

Hint: a) what kind of lines NEVER cross? b) Use the point-slope form of your equations: y=mx+b

OpenStudy (anonymous):

Parellel lines?

OpenStudy (anonymous):

Good, so from the point-slope form of those two equations the m coefficient in front of the x variable tells us the steepness or "slope" of the lines. To prove that two lines are parallel we simply need to prove that they have the same slope. I'll do the first equation. \[-2x + y = 5\] -->|[y=-2x + 5\] So the slope of the first line is m=-2 and it intercepts the y-axis at y=5. Now you do the second line.

OpenStudy (anonymous):

Ok so... 4x -2y = 9 y= -2x - 9 ?

OpenStudy (anonymous):

Careful, your first step is to subtract "-4x" from both sides. (The 9 is positive.) \[-2y=-4x+9\] An easy way to think of this is to flip the sign of the term that you want to move and to re-write it on the other side of the equal sign.

OpenStudy (anonymous):

Yikes. I actually think I'm starting understand all this. Thank you!

OpenStudy (anonymous):

\[{\frac{-2y}{-2}=\frac{-4x}{-2}+\frac{9}{-2}}\] Now we want the coefficient in front of the y to be "1" so we divide the "-2" through both sides.

OpenStudy (anonymous):

Remember a negative over a negative is a positive. \[y=2x+\frac{9}{-2}\]

OpenStudy (anonymous):

Err... I just spotted a typo on when I did the slope-intercept form of the first equation. It should be: \[y=2x + 5\] ... So. Are the lines parallel? :-)

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