Graphical Solutions

Can someone help me? I have been looking around on the Internet and have been asking friends but have recieved no clear explanation. The direction say "Solve each system graphically"

The problem itself is something like: x+y=5 with something like x-y=1 directly beneath the first problem and all that is one question.


Then next to it is an empty graph. Then under the graph, there is:

(_,_)


This is in a reiew packet for the summer because i am going into algebra 2 and its supposed to show what we remember from 2 years ago. The thing is, i dont remember this at all!! I have 6 pages of this stuff and if i cant do it, ill most certainly start off school with a 70% or less. Any help at all will be greatly appreciated!

"Solve graphically" simply means plot the two equations (lines) on the graph. The solution (answer) is the point of intersection. You have to draw the lines very carefully/accurately to get the right answer. Then just write the coordinates of the point in the space provided: (_,_)

Simple, no? Hope that helps.

You must learn to draw the graphs of the equations. This can be arduous, but it doesn't have to be. If all one has is linear functions (lines), one can solve for y, putting things in slope-intercept for, so that they can be graphed on the same set of coordinate axes. After graphing things, one can just look where they intersect, if they do, and write down the coordinates of the intersection. If the solution is NOT an integer, well, the precision can be lacking. Just give it a good shot.

oh....*slaps forehead*

I suppose i must look really stupid right about now...

Anyways, thanks alot!

And just another stupid question, its (x,y) right? Just making sure.

And also, is it possible to put a frational coordinate? (ex) (2/3, 5)?

And so, for my example, the answer would be 2,3.....right?

Stupid: We're not about stupid, here. We're about learning.

Fractions: Sure. I tried to cover that in my last comments.

(2,3): On THIS problem. What of the next one...?

ok, the next one is 2x-y=2 and x+2y=6

Im getting it simplified to y=2x-2 and y=-1/2x+3

But when i graph it....i dont know where it goes, i think i did something wrong, ill try again...

ok, i have a question,, how come on my first problem: y=-x+5, the starting point was plotted on the x line while y=x+1 was plotted on the y line?

On my second question, i simplified the question. After tireless minutes of trying, i didnt get it. Then i took out my graphing calculator and graphed the simplified forms. The calculator plotted both starting points on y line! I dont understand this... And according my caluclator's methods, the answer is (2,2).

TheKeyboardist said:

how come on my first problem: y=-x+5, the starting point was plotted on the x line while y=x+1 was plotted on the y line?

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These are lines. They have no "starting" point. Please clarify what you mean, keeping in mind that we can't see the pictures you've drawn.

TheKeyboardist said:

On my second question, i simplified the question.

Click to expand...

How? What did you do? What did you get?

TheKeyboardist said:

The calculator plotted both starting points on y line! I dont understand this.

Click to expand...

Since we can't know what you punched into your calculator, and since we can't see your calculator's screen, you're going to have to clarify the situation. What do you mean by "starting points"? What did you enter into your calculator? What are the screen settings? And so forth.

Eliz.

Graphing Linear Equations, Solving Linear Systems

Do you know the Slope-Intercept Form and what its parameters represent? This will answer all the question you have presented.

It is very easy to change the "window" or the visible graph limits. Do not let visual deficiencies confuse you. You may not SEE it extend to the y-axis, but that does not mean that it doesn't extend to the y-axis.

isnt tthe "+5" in y=-x+5 the point you start your line and you make your slope from there?

I took x+y=5 and x-y=1 and made it into the y= form.

I took the y= simplified forms and punched them into the calculator and pushed "graph"after i put those 2 in. And the lines drew on the graph. Its a TI-83 Plus. Theres a button that says "Y=" and thats where i put the y forms in.


Ive heard of Y-Intercept, the starting point but im not sure of the Slope Intercept....

oh, i see it, in the graph above that tkhunny drew up, it seems as if the y intercept was placed on the x line but now i see that its on the y line as well. So i got a little confused thinking the point should go on the x line.

So do both points always go on the y line?

TheKeyboardist said:

So do both points always go on the y line?

Click to expand...

Which points? What is the "y line"? Do you mean the "y-axis"? If so, only the y-intercept would be on the y-axis (as this is implicit in the definition of "y-intercept"). What is the other point?

Eliz.

oh! i see! I meant the 2 y intercepts. I keep calling the axis a line for some reason....

Ok, thanks alot guys! Im done the section finally!