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Question 1157052: Solve the system using the addition method.
1.11x-5y=10
13x-7y=2
Found 3 solutions by Alan3354, ikleyn, MathTherapy:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! 11x-5y=10
13x-7y=2
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The addition method is the elimination method.
One of the variables is eliminated.
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Multiply the 2 equations by something that makes the coefficients of one of the variables the same.
I would multiply the 1st by 7 and the 2nd by -5.
Then add them. That's "addition."
Answer by ikleyn(52784)  (Show Source):
You can put this solution on YOUR website! .
11x - 5y = 10 (1)
13x - 7y = 2 (2)
The idea of this method is to multiply each equation by some number in such a way
to make the coefficients at some variable EQUAL (or OPPOSITE).
Then by subtracting equations, we can DELETE this variable in the resulting equation.
So, we will get in this way SINGLE equation with ONLY ONE unknown, which is easy to solve.
Looking into the given equations, you see that the better and the simplest way is to multiply
first equation by 7 and the second equation by 5.
You will get then these two equations
77x - 35y = 70 (3)
65x - 35y = 10 (4)
Do you see these terms "35y" in each equations ? They are exactly that we were going to provide (and we provided them (!) ).
Now from equation (3) subtract equation (4). The terms "-35y" will cancel each other,
and you will get ONE SINGLE equation for the unknown x ONLY (!)
77x - 65x = 70 - 10.
Simplify and solve it, as the equation with only one unknown x
12x = 60.
x = 60/12 = 5.
The last step is to substitute this value of x into EITHER of the two original equations.
You will get then an equation for "y" only, and you should solve it to get y.
Do it on your own.
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I completed my explanations.
Now I ask you 1) if you do understand everything in my post,
and 2) please inform me if you there able to complete the solution.
If you will post to me, PLEASE refer to the problem's ID number 1157052;
otherwise, I will not know to which problem your message does relate.
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In this site, there is the lesson, explaining this technology in all details.
- Solution of the linear system of two equations in two unknowns by the Substitution method
- Solution of the linear system of two equations in two unknowns by the Elimination method
It is the SECOND lesson in this short list.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Systems of two linear equations in two unknowns".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
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It is my response to your question : x = 5, y = 9.
You may check it by substituting the values into original equations.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
Solve the system using the addition method.
1.11x-5y=10
13x-7y=2
Another one of these?
I guess if you keep posting the sane types of problems and people keep helping you/doing them for you, I guess you'll never want to do them yourself.
So, the question becomes, why are they still doing these problems for you, if you've been shown countless times how to do them?
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