Solve by the graphic method:
y=(2/3)x+3 and 2x-3y=-9

Question

Solve by the graphic method:
y=(2/3)x+3 and 2x-3y=-9

koikkara · Answer

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shamim · Answer

i think ur given 2 lines r parralel with each other. is not it

anonymous · Answer

Yah it is parallel but how to solve it?

shamim · Answer

so u hv no solution

shamim · Answer

2 lines will not cut at any points

anonymous · Answer

Hmm, but can i get the value of x and y? Or not?

shamim · Answer

no u will not get any value of x and y which will satisfy both 2 lines

anonymous · Answer

Oh thanks!

anonymous · Answer

To solve graphically, you have to graph each equation.  The solutions is the point(s) where they cross each other.  Both are linear, so you graph should be 2 straight lines.  If they are parallel, then there is no solutions, but knowing that is not enough.  You have to show it graphically.

Do you know how to graph the equation of a line?  There are ways to do so.  One is by plotting points and the other is by using the slope and y-intercept.

shamim · Answer

welcome

anonymous · Answer

I just substitute the value of x as -3,0,3 and i get y= 1,3,5 i have ordered pairs (-3,1),(0,3),(3,5) then i graph the values, is tha correct?

shamim · Answer

ya u r right

shamim · Answer

just now i solved  ur 2 equation of line

shamim · Answer

ur given 2 lines r same line

anonymous · Answer

You substitute any values you want, so those values work.  In the second equation, I would "solve for y" first as it is easier to plug in values for x and solve for y.
   2x - 3y =9                    Get the term with y alone
- 2x              -2x              Subtract 2x to get y alone
        - 3y  = -2x + 9

Dividing each term by 3, we get:
             $$y=\frac{ 2 }{ 3 }x-3$$

The values you chose to plug in were smart.  Any number divisible by 3 will make the fraction "disappear"

anonymous · Answer

see here u can find distance of separation between the lines

anonymous · Answer

may i tell u how or u know it ?

anonymous · Answer

Were you told to find the distance of separation?  I thought you were just told to solve.  When you graph them, you can see that they are parallel and you just write "no solution"

anonymous · Answer

infinite solutions, its same linee

anonymous · Answer

both equations are same

anonymous · Answer

You are right!  I was thinking the y-intercepts had different signs, but they don't so they are exactly the same line!

anonymous · Answer

the answer is infinitely many solutions

anonymous · Answer

yep

anonymous · Answer

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anonymous · Answer

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