SOLUTION: I cannot figure out how to solve systems by graphing. I have read and read but am so confused. I need to solve the system 2x+y=2; 6x+4y=12. Please help me figure out the answer

Algebra.Com
Question 632161: I cannot figure out how to solve systems by graphing. I have read and read but am so confused. I need to solve the system 2x+y=2; 6x+4y=12.
Please help me figure out the answer and show/explain how. Thanks.
Found 2 solutions by josmiceli, ewatrrr:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
You have 2 straight lines. The best way to get an
idea what they look like is to convert the equations
from the standard form ( as they now are ) into
the slope-intercept form
---------------------

(1)
and


(2)
---------------------
(1) and (2) are now in the form
where = slope and = y - intercept
---------------------
In (1),
In (2),
Both slope are negative, which means they go from
upper left to lower right on the graph, opposite to
what a positive slope does
---------------------
gives you a point for free on each line. It
is the y-intercept point which is (0,b), or
(0, 2) for equation (1)
(0,6) for equation (2)
--------------------
Now you just need 1 other point for both lines, and
since 2 points determine a line, you can draw
each line. Where the lines intersect is the solution
to the system of lines
--------------------
To find the other point, just plug in any value for
, and read off the value for
For example:
(1)
I'll pick
(1)
(1)
So, I have the point (1,0)
and
(2)
I'll pick
(2)
(2)
(2)
So, I have the point (2,0)
---------------------
Now you have this information about the lines:
Line (1):
(0,2)
(1,0)

----------
Line (2):
(0,6)
(2,0)

----------
And that's all you need
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
 

Hi,

Solve the system by putting each of their graphs on the same graph

the point they intersect at: (-2,6) is the solution for this system



If You are having difficulty graphing each of the linear equations:

find at least 2 (x,y)points for each and connect pair of the 2 points with their

respective line 

2x+y=2   x = 0  ⇒ y = 2,  y = 0  ⇒ x = 1  (0,2) and (1,0) on this line

6x+4y=12   x = 0  ⇒ y= 3,  y = 0  ⇒ x = 2  (0,3) and (2,0) on this line

 

RELATED QUESTIONS


Hello,
  I have recently started learning about the systems of linear equations. I... (answered by Earlsdon)

ok so i have a final on tuesday thats worth 65 percent of my grade. I am failing the... (answered by Alan3354)

I am having so mush trouble trying to figure out first what to do with this problem, I... (answered by ewatrrr)

I need to solve for X. The problem is 2x^2+24=x^2 i then moved the x^2 so that the... (answered by Fombitz)

I would appreciate it so much if someone could show me how to draw and solve the Venn... (answered by math-vortex)

I must solve the system of equations by graphing. 
x-y=-2
x+y=12

I cancelled out the  (answered by Alan3354)

I am trying to work a problem and not sure if I am on the right track.  

The problem... (answered by jim_thompson5910)

can I have some step by step examples of how to solve linear systems using elimination... (answered by mananth)

I am very new to algebra and I do not know how to read or solve the... (answered by Alan3354)