Question 239150: Can someone please help me? ----- (elimination method)
The assignment is on the elimination method - and I don't understand why it is not coming out evenly.
2/3x+y=-5/3 and x-1/3y=-13/3
Found 2 solutions by rapaljer, checkley77:
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! 2/3x+y=-5/3
x-1/3y=-13/3
It may help to clear the fractions by multiplying each equations by the LCD of 3.
3*2/3x+3*y=3*-5/3 and 3*x-3*1/3y=3*-13/3
2x+3y -5 and 3x -y =-13
2x+3y =-5
3x-y=-13
To eliminate the y terms, you need to multiply both sides of the second equation by 3.
2x+3y = -5
9x-3y = -39
Add the equations together:
11x=-44
x=-4
Substitute x=-4 back into the first equation after you cleared the fractions:
2x+3y =-5
2(-4)+3y =-5
-8+3y =-5
Add +8 to each side:
-8+8+3y=-5+8
3y=3
y=1
Check in the second equation, which was
3x-y=-13
3(-4)-1=-13
-12-1=-13 It checks.
The final answer is the point (-4,1).
I suppose technically, I should have checked by subsituting the values of x and y back into the ORIGINAL equations, with FRACTIONS! You may want to do this yourself. In fact, your teacher may REQUIRE it!! However, I personally think that is just TOO TEDIOUS! I'm retired, so I don't have to!!!
For additional help with this topic of Solving Systems of Equations, please see my own website. To find my website, do a "Bing" search or a "Google" search for my last name "Rapalje". Near the top of the search list, look for "Rapalje Homepage." Near the top of my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose the link "Basic Algebra" and look in "Chapter 4" for "Section 4.07 Systems of Equations." In this section, you will find my own non-traditional explanation especially designed for students that have trouble understanding their own books. My own explanations, together with examples and exercises, are also supported by my "MATH IN LIVING COLOR" pages in which I've solved the hardest problems IN COLOR.
In addition to these, I have a LOT of similar resources, both in written and video form, that may help you on a number of topics. Anyone can send me an Email at rapaljer@scc-fl.edu, and I'll be glad to tell you about the topics and pages that are available on the website.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
Answer by checkley77(12844)  (Show Source):
You can put this solution on YOUR website! 2/3x+y=-5/3 multiply this equation by 1/3 & add.
x-y/3=-13/3
2x/9+y/3=-5/9
------------------
x+2x/9=-13/3-5/9
(9x+2x)/9=(-13*3-5)/9 cancel out the denominators.
11x=-39-5
11x=-44
x=-44/11
x=-4 ans.
-4-y/3=-13/3
-y/3=-13/3+4
-y/3=(-13+4*3)/3 cancel out the denominators.13+12
-y=-1
y=1 ans.
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