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Question 1102904: Solve the problem using the substitution method
7x-9y=-8
3x-y=16
What is the solution set for x and y?
Found 5 solutions by Alan3354, Gerwally, greenestamps, ikleyn, richwmiller:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Solve the 2nd equation for y.
Sub for y in the 1st equation.
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Answer by Gerwally(2)  (Show Source):
You can put this solution on YOUR website! The easiest way is to use the 2nd equation and solve for y. This avoids working with fractions.
Adding y to both sides gives 3x=16+y, and then subtracting 16 from both sides gives y=3x-16.
Substitute this value for y in the first equation, getting 7x-9(3x-16)=-8. Multiplying you get
7x-27x+144=-8, then -20x+144=-8. Subtract 144 from both sides gives -20x=-152, then dividing both sides by -20 gives x=7.6. Substitute 7.6 for x in first equation gives 7(7.6)-9y=-8, then multiplying gives 53.2-9y=-8 Subtract 53.2 from both sides leaves -9y=-8-53.2 or -9y=-61.2 Dividing both sides by -9 gives y=6.8 solution is x=7.6 and y=6.8
Check: Substitute both values into each equation. 7x-9y=-8 or 7(7.6)-9(6.8)-8 0r 53.2-61.2=-8 0r
-8=-8. Check! In second equation 3x-y=16 substitute 3(7.6)-6.8=16 or 22.8-6.8=16 or 16=16 Check!
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Both of the other tutors that have responded to your question so far have chosen to use substitution to solve the pair of equations. One of them even stated that substitution was the easiest way.
Easiest for her, maybe -- but not for everybody.
In particular, whenever the two equations are given in this form (Ax+By=C), solving by elimination is fastest and easiest for me.
For this example with equations  and  , I will multiply the second equation by -9 and add the resulting equation to the first equation, eliminating y. Then I can solve the resulting equation for x; and after I know the value of x, I can use it in either of the original equations to find the value of y.
Answer: x = 7.6, y = 6.8
Dear tutor ikleyn --
What I'm getting tired of is your unjust criticism of my inputs to students' questions.
When, in a response, I say I prefer a different method than what another tutor uses, that does NOT NOT NOT mean I am saying, as you put it, "they all are bad, I am the best . . . ".
Different people find different methods for solving problems to their liking; not everybody should solve a particular problem a certain way.
When I see a tutor's response to a question that uses a method of solution that is harder for me than another method, I will not hesitate to supply a response showing an alternative solution method.
Yes, I overlooked the fact that on this problem the instructions were to solve by substitution. But there is NOTHING in my response that was derogatory about tutor Gerwally's response.
In your criticism of my response, you said that by supplying a solution using the elimination method I was implying that I thought tutor Gerwally was saying that substitution was the best method for solving the problem and that he was wrong. That is not at all the case; I'm surprised that someone with your intelligence would come to such a conclusion.
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
I.
Dear tutor @greenestamps,
your reaction to the post by @Gerwally surprise me . . .
The original post asked for the substitution method - and the tutor @gerwally solved the problem exactly as it was requested.
The tutor @Gerwally said that the easiest way is to start from the second equation and to express "y" from there,
and he is absolutely right in it.
You, in your response, attributed him the words ". . . that substitution was the easiest way", although he does not state it.
And then you turn on your usual mantra "they all are bad, I am the best . . . ".
Or ". . . I personally prefer other (or my own) method".
Honestly, I just tired of it. It is not an adequate tone for tutor's posts.
Your solutions are perfect sometimes // or even OFTEN.
I would be amazingly good if your tone was in the same perfect mode.
II.
Dear tutor @Gerwally !
Your debut was PERFECT, and we are happy to have a professional teacher in this forum !
WELCOME ! !
Answer by richwmiller(17219)  (Show Source):
You can put this solution on YOUR website! We, tutors, used to have a forum on this website to discuss "tutor business.
It was trolled by students with absurd comments. And so it was put out of commission. There is still a link to it but it does not work.
Tutor Greenestamps,
I appreciate your alternate approaches to the math problems.
I believe you misspoke at least twice on this particular problem.
First, as you acknowledged, the original problem asked for a solution using substitution.
Secondly, I believe you misread tutor Gerwally's statement about the easiest way.
You stated, "One of them even stated that substitution was the easiest way."
I believe tutor Gerwally was talking about what would be the easiest approach given that he was going to use substitution as requested.
Tutor Gerwallystarted out saying "The easiest way is to use the 2nd equation and solve for y. "
Tutor Ikleyn stated:
"The tutor @Gerwally said that the easiest way is to start from the second equation and to express "y" from there"
Let's all relax,take a deep breath and try to get along.
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