Hi Dolly. Are you familiar with Elimination or Substitution methods, for solving a system of two equations? Those are two methods taught in beginning algebra.Please tell me how to even begin
So I have to use the Elimination method right? I'll solve and share my answer asap.Hi Dolly. Are you familiar with Elimination or Substitution methods, for solving a system of two equations? Those are what's taught in beginning algebra.
When we use either of those approaches, sometimes the variables end up disappearing -- leaving us with a single equation that is obviously true, like 5=5.
Whenever that happens, it indicates that the system has infinite solutions. Graphically speaking, it means that the two given equations both graph as the same line (i.e., the equations are equivalent).
There are hundreds of lessons and worked examples online. Google keywords elimination method. Let us know, if you see anything you don't understand.
is this correct? if yes, then what do I do after this.. how do I prove whether the equation has many solutionsYou may use either elimination or substitution.
We may have cross-posted, as I had just added some information to my first reply. Did you see the tip?
nopes, I didn't go through any of the worked examples.You copied the second equation incorrectly. The fraction is 5/6.
The elimination method involves eliminating one of the variables. Did you study any of the worked examples?
Before adding (or subtracting) the two equations, you first need to adjust coefficients for one of the variables.
24a - 30b = 1
120a - 150b = 5
Now, if the coefficients on variable a were opposite numbers, then adding the equations would eliminate variable a (because opposites add to zero).
But, those two coefficients are not opposites. They are 24 and 120.
What number could you multiply the first equation by, to change 24a into -120a?
Do that, and then add the equations.
thank you so much! in school we were taught that the sign of second equations shouldn't be considered like if its + we automatically change it to - and so on.You chose to obtain 120a in both equations, instead of my suggestion to get opposites 120a and -120a. That's okay, but you can't eliminate by adding 120a+120a. When the coefficients are the same, then you eliminate by subtracting equations (because 120-120 gives zero).
By the way, you didn't add your b terms correctly (-150 plus -150 is -300).
So, after multiplying the first equation by 5, did you notice that your two equations were the same? Subtracting one from the other yields 0=0.
That indicates infinite solutions.
You need a lot more practice. Study some lessons, and work through the examples. That's how we learn.
That's wrong. When using the elimination method, it is VERY important to consider the signs of terms in BOTH equations.we were taught that the sign of second equations shouldn't be considered
Yes, but I'd also instructed you to change 24a into -120a. You didn't follow that instruction. You'd changed 24a to +120a, instead. THAT is why we needed to switch to subtraction. Please slow down and pay closer attention.You were the one who told me to add the equations after multiplying.
Yup. Similar to showing that both simplify to the same equation (4a-5b=1/6).I would multiply the 1st equation ... by this magic number and confirm that both equations now are identical.
Hi Dolly. You hadn't provided any context, so we assumed you were a student (please see 'Read Before Posting').I am not in any class so how should I answer this! all I have is the question(s) at my end.
That English is not clear, Dolly, but Jomo did not say that fractions are called magic numbers. He was referring to a case-specific factor that changes one equation to match another. In other words, when Jomo said 'magic' he meant 'special'. Just like 5 was a special factor, when it changed 24a-30b=1 to match the other equation 120a-150b=5.I was legit today years old to know that fractions are called magic numbers
Why are you interested in this exercise?Neither do I have the textbook nor am I in any class.