ErinWeeks
  • ErinWeeks
Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. 4x - 3y = 6 -12x + 9y = -24
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
hint: 1. multiply first equation by 3 on both sides 2. add the results to the second equation. 3. you should be able to get rid of one of the variables. 4. once that's done, solve for the remaining varaible. 5. to ge the other variable, substitute your solution into any one of the original equation.
ErinWeeks
  • ErinWeeks
@djaydeej88 im sorry could you show me i honestly got stuck at 1. so would one be 4x-9y=18?
ErinWeeks
  • ErinWeeks
@djaydeej88 ???

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anonymous
  • anonymous
As djay did above, one of the methods to solve this question is to eliminate one of the variables so that you can first solve for the other. There are two special cases to look out for though: (1) One of the equations can be changed so that the LHS (the side with all the variables) is equal to the other equation but the RHS is not. This is the case where there are NO solutions. (2) One of the equations can be changed to the other equation. This is the case with INFINITE solutions. And remember that what you do to one side of the equation you must also do to the other! In this case, if we multiply the first equation by -3, you get -12x + 9y = -18 and now we have case (1) above.
ErinWeeks
  • ErinWeeks
@Erin001001 i am sorry so i had to leave earlier family issues.. can you finish helping me with this? so would the answer be none?
ErinWeeks
  • ErinWeeks
@Psymon can you help me please?(:
Psymon
  • Psymon
Answer is none it seems. But do you know why?
ErinWeeks
  • ErinWeeks
no i dont thats what i need some to explain!
Psymon
  • Psymon
So guessing none of what was said above made much sense, eh?
ErinWeeks
  • ErinWeeks
it really didnt thats why i asked you .. usually you make sense to me. lol
Psymon
  • Psymon
Well, it says method of your choice, which means substitution or elimination (addition). Now, a lot of the time the first thing you check for is if the x's or the y's look like multiples of each other. For example, if I invent two equations like: 3x -9y = 18 5x + 27y = 24 Now, it may not always be obvious, but what I notice is that 9 times 3 is 27. And since we have a -9y and a positive 27y, I can multiply thetop equation by 3 to give me 9x - 27y = 54 5x + 27y = 24 Now I can add the two equations and eliminate y. So if you can see that a variable might be eliminated easily, you probably want to choose elimination method. Now on to what we actually have: 4x - 3y = 6 -12x + 9y = -24 So again, the first thing Im checking for is if either the x's or the y's are multiples of one another. If you notice, we have a +4 and a -12. Well, 4 times 3 = 12, so that's pretty easy to see. And you can maybe see this with the y's, too. We have a -3y and a +9y. Well, 9 is 3 times 3, so the y's can match up easily as well. So it looks like elimination is a good strategy. Now just to clarify, when we do the elimination method, we are multiplying one or both of the equations (all of the numbers in each equation) by some number in order to get x's and y's in both equations to be the same number, but of opposite signs. After you accomplish this, you then add both equations together. X's get added to X's, y's to y's, numbers to numbers. So the goal is to get a 3x -3x or 9y -9y something as to where if we were to add the two, they would become 0. So now like I mentioned, it does look liek x's can be matched up pretty easily. So I currently have: 4x and -12x If I multiply 4x by 3, I will have 12x and -12x. Because of this, I'm going to multiply that whole top equation by 3. Doing this I get: 12x - 9y =18 -12x + 9y = -24 Now I add the two equations. So I have -12x + 12x = 0. -9y + 9y = 0. 18 + -24 = -6 to get a final result of 0 +0 = -6..... Clearly there is no possible way this can happen. Whenever you get two things on opposite sides of the equal sign that are never equal, there are no solutions. Kinda make sense?
ErinWeeks
  • ErinWeeks
Makes a lot more sense that you showed me and explained i get it!
Psymon
  • Psymon
Okay, awesome ^_^

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