Question 12338: Hi Tutors: ( Rapalger, Abbie, Longjonsilver, whomever has the time)
I asked for help last night with this problem and it seemed like nobody was available to help me. So I am trying again. The topic is SYSTEMS OF EQUATIONS IN TWO VARIABLES. Please show me how to solve this equation graphically, classify the system as consistent or inconsistent and classify the equation as dependent or independent? Thanks in advance. f(x)=x+1, g(x)= 2/3x I think I am allowing the fraction to throw me off!
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! here is a link to an explanation on consistency and dependency...
http://mathforum.org/library/drmath/view/62538.html
When you say graphically, to me that means you have been asked to plot the graphs properly, rather than sketch them and work out just the salient points, like axes-intercepts and roots.
So, to graph them, pick values of x, put them in both equations (seperately) to get 2 sets of y-values. Then plot.
f(x)
y=x+1 is a straight line like / that goes through the y-axis at y=1.
now g(x)...i am not sure how to read this..you need to use brackets...
either
1. y=(2/3)x is another straight line passing through the orign
OR
2. y=2/(3x) is a 2-part curve, broken at the x=0 and y=0 lines
if g(x) is 1, then there is 1 solution... one point where the 2 equations cross
if g(x) is 2, then there will be 2 solutions... two points where the 2 equations cross.
hope this helps
jon.
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