Question 457527: Can someone help me solve the solution of the system by using the elimination method to find the solution?
x + 5y = 20
-x + 8 = 19
Found 5 solutions by mananth, ikleyn, MathTherapy, mccravyedwin, n2:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! x+5y=20 .............1
-x+8y=19 .............2
multiply (1)by -8
Multiply (2) by 5
-8x-40y= -160
-5x+40y =95
Add the two equations
-13x=-65
/-13
x=5.00
plug value of x in (1)
x+5y=20
5+5y=20
5y=20-5
5y=15
y=3
Answer by ikleyn(53538)  (Show Source):
You can put this solution on YOUR website! .
Can someone help me solve the solution of the system by using the elimination method to find the solution?
x + 5y = 20
-x +8y = 19
~~~~~~~~~~~~~~~~~
When somebody solves such a system by the elimination method, the major question
is to choose a right strategy. The strategy which @mananth chooses in his solution,
is difficult to call a rational or a reasonable. He makes tons of unnecessary calculations,
which is easy to avoid if to use a rational strategy.
Your starting equations are
x + 5y = 20 (1)
-x + 8y = 19 (2)
Add the equations. The terms 'x' of the first equation and '-x' of the second equation
will cancel each other, opening the way to a short and clear straightforward solution
5y + 8y = 20 + 19,
13y = 39
y = 39/13 = 3.
Now from equation (1)
x = 20 - 5y = 20 - 5*3 = 20 - 15 = 5.
ANSWER. x = 5, y = 3.
CHECK. Substitute these values into equations to make sure that the answer is correct.
Solved.
This way of solving by elimination is natural.
The way which @mananth promotes/uses in his post is (a) unnatural and (b) is a   to teach.
/\/\/\/\/\/\/\/\/\/\/\/
This my addition is specially for tutor @MathTherapy and for other tutors, who want to know the truth.
The truth is that @mananth solutions are not the solutions produced by a living person.
They are the solutions produced by a computer code.
I started checking his solutions systematically somewhen in November-December of 2025.
After checking approximately 70 of his solutions, I noticed repeating patterns in his solutions.
Very often these patterns were errors that a living person in healthy mind would never make.
It was a starting point for me to suggest that @mananth is a computer code.
See my post under this link
https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.434949.html
https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.434949.html
where I first time formulated this my idea.
The more I submerged in his solutions the more I became sure that this is true.
Now, after checking about 1000 of his solutions, I am 129% convinced in it.
The other side of this truth is/was that many hundreds (if not thousands) of the same type Math problems,
that were posted to this forum and solved by @mananth, were posted not by real students/visitors,
but were created and posted with the only goal to train this code in solving them, to demonstrate
the abilities of the code in solving such problems, to get checking from free of charge voluntary tutors
and, ultimately, to build a base of knowledge (= a base of solutions) for artificial intelligence.
Answer by MathTherapy(10680)  (Show Source):
You can put this solution on YOUR website!
Can someone help me solve the solution of the system by using the elimination method to find the solution?
x + 5y = 20
-x + 8 = 19
This is the MOST RIDICULOUS and DUMBEST way I've ever seen an EXTREMELY SIMPLE solve-by-elimination
equations-system, solved.
BTW, is this REAL?
Answer by mccravyedwin(419)  (Show Source):
You can put this solution on YOUR website!
This is written:
x + 5y = 20
-x + 8 = 19
but it's being solved as if it were
x + 5y = 20
-x + 8y = 19
Is that second term in the second equation supposed to 8, or 8y?
Edwin
Answer by n2(35)  (Show Source):
You can put this solution on YOUR website! .
Edwin,
about 40 years, I worked as a computer programmer, developing computer codes for my own researches
and for customers. After many years of working, I learned the truth: a good programmer knows better
than a customer, what the customer needs.
Working about 15 years at this forum, I can say similarly that I know better than any visitor
what this visitor wants to say or wants to express in his post.
Physicists who work every day with elementary particles on accelerators and observe tracks
of these particles, identifying known and unknown particles, have their professional proverb
"It's shameful to doubt when you know for sure".
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