Question 26347: My son is having problems with this type of equation. He has to find out if the linear equation is consistent or inconsistent.Dependant or independant. Example: x+y=4 5x+y=8 How do you graph this equation. How do you work 5x+y=8 to know where to draw the second line of this equation.What would the graph look like .Thanks
Found 2 solutions by venugopalramana, queenofit:
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! SEE THE FOLLOWING TO GET AN IDEA OF THE TOPIC.IF STILL IN DIFFICULTY PLEASE CONTACT ME AND I SHALL HELP FURTHER
AS REGARDS GRAPHING GIVE DIFFERENT VALUES TO X AND FIND Y FROM THE GIVEN RELATION .SEE BELOW
I EQN....X+Y=4
X.............0.........1...........2...........3..............4........ETC...
Y=4-X.........4.........3...........2...........1..............0.........ETC
II EQN.....5X+Y=8
X...........0...........1............2.............3......ETC.........
Y=8-5X......8...........3............-2............-7.....ETC...........
THE GRAPHS WILL LOOK LIKE THIS.
THE 2 LINES INTERSECT AT X=1 AND Y=3 WHICH IS THE UNIQUE SOLUTION TO THESE EQNS.THAT IS THEY ARE CONSISTENT AND INDEPENDENT.IF THEY ARE DEPENDENT YOU WILL GET ONE IDENTICAL LINE FOR BOTH EQNS.THAT IS THEY HAVE INFINITE SOLUTIONS ON THAT LINE. IF THEY ARE INCONSISTENT YOU WILL GET 2 PARALLEL LINES WHICH DO NOT INTERSECT AND HENCE THERE IS NO SOLUTION
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What is a coinciding equation?
1 solutions
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Answer 13848 by venugopalramana(791) on 2006-01-28 11:16:56 (Show Source):
consider these 2 eqns
x+y=2...........i
2x+2y=4.........ii
if the first eqn is given to us ,the second one can be derived by us by multiplying the first eqn. with 2 on either side. so the second eqn.does not give us any additional information ,but is a derivative or dependent eqn. of eqn.i.read the following for additional related information.in case of more than 2 or for that matter any number of equations , if one or more of them could be sinilarly derived by a suitable combination of other eqns.,then we say they or dependent eqns.
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When using gaussian elimination, can an inconsistant solution have a general solution? i worked out the matrix and came to a spot where 1=-3 and 1=10.4 (inconsistant 1 can't equal 2 different solutions); would there still be a way to formulate a general solution such as x=(2-4x,2-3x,x,0) = (2,2,0,0) + x(-4,-3,1,0)
I hope this is enough information to clearly explain my question. thanks
I THINK YOU ARE CONFUSED BETWEEN ...INCONSISTENT,AND DEPENDENT EQUATIONS.
AS THE NAME IMPLIES AN INCONSISTENT SET OF EQUATIONS HAS NO SOLUTION AS THEY ARE INCONSISTENT.FOR EXAMPLE
X+Y=2
2X+2Y=3....HENCE THERE IS NO QUESTION OF GETTING A GENERAL SOLUTION FOR THAT BY ANY METHOD GAUSSIAN ELIMINATION OR ANY..
CONSISTENT AND DEPENDENT EQNS.HAVE INFINITE SOLUTIONS GIVEN BY A GENERAL FORMULA AS YOU HAVE MENTIONED..FOR EX.
X+Y=1
2X+2Y=2....THE GERAL FORMULA IS Y=1-X...OR (X,1-X)IS A SOLUTION SET..LIKE (1,0),(2,-1) ETC....
FINALLY CONSISTENT AND INDEPENDENT EQNS.HAVE UNIQUE SOLUTION..FOR EXAMPLE
X+Y=2
X-Y=0...HAVE ONE UNIQUE SOLUTION X=1 AND Y=1
NOW YOU CAN USE GAUSSIAN ELIMINATION TO THE 3 EXAMPLES ABOVE AND SEE WHAT YOU GET.IF YOU STILL AVE DIFFICULTY COME BACK
Answer by queenofit(120)  (Show Source):
You can put this solution on YOUR website! first lets look at x+ y = 4
by writing the equation in slope-intercept form (y=mx+b)
y= -x + 4 you can see that the y intercept is ( 0, 4), this is your first point for this line. Moreover, because the slope, m=-1, (m = your slope and m is the number in front of your x, in this case it is an -1 represented by the - in front of your x). So this line would fall one unit for each unit it moves to the right. In other words, plot (0,4) then move one unit to the right and one unit down and plot another point (1,3) and so on, moving one to the right and one unit down because of the neg x.
As for 5x+y=8, you would do this in the same mannor. put the equation in slope intercept form y=mx+b
y=-5x+8
your first point would be the y intercept which is (0,8) in this case. since your slope is -5, this line would fall 5 units for every one unit it moves to the right just like we did it above. let your son graph these and see if he can figure out if they are depentant or indepentant of each other from the graph. this is most likely what the instructor wanted him to do.
Tips for graphing :
a) when your slope (m) is positive, the line rises from left to right
b) when your slope (m) is zero, as in y=2, the line is horizontal
c) when your slope (m) is negative (as in your examples), the line falls from left to right.
To find the y intercept of an equation, let x=0 and solve for y. then put it into (0,y)as your point. to find the x intercept let y=0 and solve for x, then (x,0)is your point.
This portion of his algebra is difficult to grasp, however, I cannot stress how important it is that he gets a good understanding of it. He will need it for the higher maths in college, I tutor at college and in High school as well as on this website and you would not believe the amount of students who have graduated high school without the understandings of the math concepts they need to suceed in the college courses. You are a great parent to help him!!!!He just doesn't know how much. I wish all my students had a parent like you.
If you need further assistance, please post again and I will try to help in anyway that I can.
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