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Mathematics 13 Online
OpenStudy (vshiroky):

Solve by graphing

OpenStudy (vshiroky):

Nnesha (nnesha):

first you have to solve for y

Nnesha (nnesha):

can you solve both equatiosn for y ?

OpenStudy (vshiroky):

I got the points for the first as (0,4), (2,5), (4,6)?

OpenStudy (vshiroky):

and for the second I got (0,0), (0,1), (0,2)

OpenStudy (vshiroky):

oops I mean (0,0), (2,1), (4,2) for the 2nd

Nnesha (nnesha):

points?? to check it you can replace x and y by their values and see if you get both side equal

OpenStudy (vshiroky):

That's what I got my graph to look like

OpenStudy (vshiroky):

I don't know this is how someone told me to do it but I'm lost

OpenStudy (jdoe0001):

hint: \(\bf \text{"Solve by graphing"}\)

Nnesha (nnesha):

nope that's wrong

OpenStudy (vshiroky):

I have no clue then

Nnesha (nnesha):

in order to be parallel lines both equations should have same slope

OpenStudy (vshiroky):

Then I'm lost on where to start

Nnesha (nnesha):

are you sure u plugged that right into calculator ??

OpenStudy (jdoe0001):

hmmm do you know how to simplify linear equations? that is, what Nnesha said, solvinng for "y"

OpenStudy (vshiroky):

I did it myself, I don't know how to plug in a graph

OpenStudy (vshiroky):

That's what I thought I was doing

OpenStudy (jdoe0001):

so what did you get after solving each for "y" then?

OpenStudy (vshiroky):

Those are the points I got, but I guess I didn't do it right

Nnesha (nnesha):

yeah that is not right bec if you use one of order pair and plugg that into equations u are not gonna get equal side and that's mean that order pair is not solution

Nnesha (nnesha):

@jdoe0001 <-- he can hep ou i gtg now sorry its urgent ^_^

OpenStudy (vshiroky):

Ok thanks

OpenStudy (vshiroky):

For the first I got y=1/2x-4

OpenStudy (anonymous):

you need help

OpenStudy (anonymous):

hello

OpenStudy (vshiroky):

Yes please

OpenStudy (anonymous):

ok

OpenStudy (anonymous):

i have a guy that can help see math is not my subject let me give the guy a call

OpenStudy (jdoe0001):

yeap, the 1st one is correct to graph that just pick 2 points say x = 0 and use the y-intercept, or when y=0 notice that the slope-intercept form gives away the y-intercept \(\bf y=\cfrac{1}{2}x{\color{blue}{ -4}}\qquad {\color{blue}{ y-intercept}}\)

OpenStudy (jdoe0001):

and use the y-intercept, or when x=0 rather so... hmm

OpenStudy (anonymous):

@vshiroky your welcome

OpenStudy (vshiroky):

So I put 0 where x is?

OpenStudy (anonymous):

um let me call the guy again

OpenStudy (vshiroky):

@jdoe0001 for the 2nd equation I got y=1/2x

OpenStudy (anonymous):

he is coming

OpenStudy (jdoe0001):

well let us get two points, and thus 2 values for "x" let use pick say x = 0, that gives the y-intercept anyhow, which is -4 thus ( 0, -4 ) so another point , say let us make y = 0 for simplicity one sec

OpenStudy (anonymous):

k

OpenStudy (vshiroky):

I still don't understand what you mean

OpenStudy (jdoe0001):

so.. here are your two equations, and a couple of points to plot them \(\bf y=\cfrac{1}{2}x-4 \begin{cases} x=0\qquad y=-4&(0,-4)\\ \hline\\ y=0\\ 0=\frac{1}{2}x-4\to 4=\frac{x}{2}\to 8=x&(8,0)\\ \end{cases} \\ \quad \\ y=\cfrac{1}{2}x \begin{cases} x=0\qquad y=0&(0,0)\\ \hline\\ y=0\\ 0=\frac{1}{2}x\to 0=x&(0,0) \end{cases}\)

OpenStudy (jdoe0001):

notice something their slope of 1/2, is the same in each same slope = parallel lines

OpenStudy (jdoe0001):

parallel lines never touch each other, thus, a solution is when the graphs intersect no intersect, no solution

OpenStudy (jdoe0001):

hmmm

OpenStudy (jdoe0001):

hold the mayo for a sec, the 2nd equation.... is a bit off lemme do that one quick

OpenStudy (jdoe0001):

x+2y = 0 2y = -x y = -x/2 <-- minus

OpenStudy (jdoe0001):

\(\bf y=\cfrac{1}{2}x-4 \begin{cases} x=0\qquad y=-4&(0,-4)\\ \hline\\ y=0\\ 0=\frac{1}{2}x-4\to 4=\frac{x}{2}\to 8=x&(8,0)\\ \end{cases} \\ \quad \\ y=-\cfrac{1}{2}x \begin{cases} x=0\qquad y=0&(0,0)\\ \hline\\ y=0\\ 0=\frac{1}{2}x\to 0=x&(0,0) \end{cases}\) the slopes differ, one is negative, the other positive, thus they should intersect, and thus have a solution

OpenStudy (jdoe0001):

anyhow, for the one is... \(\large { y=-\cfrac{1}{2}x \begin{cases} x=0\qquad y=0&(0,0)\\ \hline\\ y=0\\ 0=-\frac{1}{2}x\to 0=x&(0,0) \end{cases}}\)

OpenStudy (vshiroky):

I have no clue what just happened

OpenStudy (vshiroky):

This is making 0 sense to me

OpenStudy (jdoe0001):

hmm what part?

OpenStudy (jdoe0001):

site is a bit laggy, so you know

OpenStudy (vshiroky):

Any of it

OpenStudy (vshiroky):

How do I graph 0,0

OpenStudy (jdoe0001):

ok... well...can you follow where we got the coordinates for each from their equation? \(y=\cfrac{1}{2}x-4 \begin{cases} x=0\qquad y=-4&(0,-4)\\ \hline\\ y=0\\ 0=\frac{1}{2}x-4\to 4=\frac{x}{2}\to 8=x&(8,0)\\ \end{cases} \\ \quad \\ y=-\cfrac{1}{2}x \begin{cases} x=0\qquad y=0&(0,0)\\ \hline\\ y=0\\ 0=-\frac{1}{2}x\to 0=x&(0,0) \end{cases}\)

OpenStudy (vshiroky):

No and I'm on my last attempt so I'm gunna get it wrong and have to do a whole new problem

OpenStudy (jdoe0001):

ok.... can you see how we get 0,-4 from the 1st equation then?

OpenStudy (vshiroky):

no

OpenStudy (jdoe0001):

ok \(\bf y=\cfrac{1}{2}x-4\qquad x={\color{brown}{ 0}}\implies y=\cfrac{1}{2}{\color{brown}{ 0}}-4\implies y=0-4\implies y=-4 \\ \quad \\ x=0\qquad y=-4\implies (0,-4)\) see it now?

OpenStudy (vshiroky):

yea

OpenStudy (jdoe0001):

what about the other values.... they were obtained by doing the same thing setting "x" or "y" to some value, in this case 0, and getting the value of the other folllow that?

OpenStudy (vshiroky):

is this right?

OpenStudy (vshiroky):

thank you. I'm not gunna do the others I don't think I can

OpenStudy (jdoe0001):

yw

Nnesha (nnesha):

why not \(\huge\color{green}{{\rm you }~\rm can !! :)}\) \(\Huge \color{gold}{\star^{ \star^{\star:)}}}\Huge \color{green}{\star^{ \star^{\star:)}}}\) try :)

Nnesha (nnesha):

@jdoe0001 thanks :)

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