Question

Part 1: Explain, in complete sentences, how you would use the graphing method to solve the following system of equations. (3 points) Part 2: Provide the solution to the system. (2 points) Part 3: Explain what the solution represents on the graph. (1 point)

3x – 6y = 12
9x + 2y = –24

Answer 1

i wouldnt use the graphing method to solve any system of equations; id simply use it as a visual aid to get me in the ballpark

Answer 2

Geometry without algebra is dumb (ask the Greeks), algebra without geometry is blind (ask the Chinese).

Answer 3

could somebody just help me learn to graph it

Answer 4

do you need all the points of each equation? or will just 2 for each one work?

Answer 5

Ok, we just want to know whether u are expected to do it all by graph only.

Answer 6

I have to do it all by graph. and two for each one will work!

Answer 7

just explain how to graph it.... then help me solve the system....and explain how the solution represents the graph

Answer 8

which 2 points do you think will be the easiest to find with these equations?

Answer 9

2 points for each equation that is

Answer 10

Do u know that they are straight lines?

Answer 11

yes they are straight lines. @amistre64 and a point on the x axis and a point on the y axis?

Answer 12

correct :)

so we use x=0 in one case; and y=0 in the other and that should give us 2 points to draw a line with right?

Answer 13

3x – 6y = 12 ; (x=0, y=?) ; (x=? , y=0)

Answer 14

how would we solve the ? do you have to solve the 3x-6y=12 twice one time for y and another time for x?

Answer 15

yes

Answer 16

the equation is a road map; use it as many times as you need.

Answer 17

(x=0, y=-2) ; (x=-3/-6 , y=0) is that it? im not quite sure

Answer 18

if your not sure; how can we chk to make sure?

Answer 19

plug it into the equation?

Answer 20

thats right; your second point there is not going to fit into the equation very well, you might want to rethink it ..

Answer 21

x=2y+4 so.... (x=0, y=-2) ; (x=4 , y=0)

Answer 22

thats better :)

now we can omit the "x=" and the "y=" parts to get our points looking like normal

Answer 23

yes then we graph them....and are those points also the the solutions to the equation?

Answer 24

those points are just solutions to ONE of the equations, namely the top equation.

Answer 25

connect the points with a line that continues thru them

Answer 26

oh okay. so 9x + 2y = –24; (x=0, y=12) ; (x=? , y=0). but when i solve for x 9 dosnt go into 24 so what would I do?

Answer 27

your first point should be (0,-12) by the way

fractions are fractions ... you best bet for an integer would be to solve for x in such a way that you can see an integer in it ...

9x + 2y = -24 ; -2y

9x = -24 - 2y ; /9

x = (-24 - 2y)/9 ;factor out a -1

x = -1 (24 + 2y)/9

now what numbers do 9 go into that we can make out of 24 + 2y ?

24 + 2(0) = 24
24 + 2(1) = 26
24 + 2(2) = 28
24 + 2(3) = 30
24 + 2(4) = 32
24 + 2(5) = 34
24 + 2(6) = 36 .. heres one ; 9(4) = 36 too

so lets try this with y= 6


x = -1* (24 + 2(6))/9
= -1* 36/9
= -1* 4
= -4 ; (-4,6) looks like a good spot

Answer 28

then for the solution i just find which point lies on both lines (intersection)