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Choose the equivalent system of linear equations that will produce the same solution as the one given below. 4x - y = -11 2x + 3y = 5 A. -4x - 9y = -19 -10y = -30 B. 4x + 3y = 5 2y = -6 C.7x - 3y = -11 9x = -6 D.12x - 3y = -33 14x = -28
So then solve the first one and write down the results you get from it. Then solve the other ones until you get the same answers. Do you know how to solve systems of linear equations at all?
no not really
Just started the unit
Here is a website to get started with them: http://www.purplemath.com/modules/systlin1.htm After you read a little and get a better understanding of them, I'll help you go through this problem.
ok i still don't fully understand
is the answer B? because thats what I got before I just want to be sure cuz i have not done this in forever
Well then let's go over the example in your question together. \[\bf 4x - y = -11 \\2x + 3y = 5\] In my opinion, the substitution method is my favorite so let's use that one first. When we use substitution, we want to get rid of either the x or y value. We do this by making those values equal to each other. In this example, I would probably choose to get rid of the x value by multiplying the bottom half by 2. \[\bf 4x - y = -11 \\2(2x + 3y = 5)\]\[\bf 4x - y = -11 \\4x + 6y = 10\] Now we are going to subtract the bottom line from the top \[\bf ~~4x - y = -11 \\-(4x + 6y = 10)\]
So what would we get from there?
Seperate the three different values. So \[\bf 4x-4x=?\\~and~\\-y-6y=?\\~and~\\-11-10=?\]
Can you solve those three things I have there? What is 4x-4x?
or does the x cancel out
No, it would be 0. The x's cancel out.
and y-y6 would be y or would it cancel out aswell
-y-6y is the same as -1-6.
Correct. And -11-10 would be?
That would be if it was -11+10. -11-10=-21
So what we have left is \[\bf -7y=-21\] Now solve for y
Correct. So now substitute \[\bf y=3\] into the top section of the problem and solve for x
The "top section" would be \[\bf 4x - y = -11\] by the way
given what you showed me me so far it would be B. 4x + 3y = 5 2y = -6 am i right?
Let's please finish solving the example
4x - 3y =-11
So then we would solve the bottom part 2x + 3y = 5
What? Solve for x in \[\bf 4x-3=-11\]
Idk how to solve for the x in this part
\[\bf 3x=9\] Can you solve for x here?
x = 3
How about this one? \[\bf 3x-3=9\]
How about this one \[\bf 4x-3=-11\] Solve it the same way as that last one.
Correct. So now we have solved the example \[\bf x=-2\\y=3\]
I suppose you could just plug those values into the options and see which ones work.
indeed and the only one that has that Is B
Are you sure? B doesn't check out with me.
\[\bf 2(3) \neq -6\]
Oh i looked at b but saw the numbers different
Then would It Be C
sorry im really tired so sorry if im not 100% in to it
I dont know really
Let's go over A \[\bf x=-2\\y=3\\~\\-4x - 9y = -19\] Plug em in and see if they work
No it wont work
i don't know how to say this, but it does work.
all I had to do was do 8-27
\[\bf x=-2\\y=3\\~\\-10y=-30\] Does it work?
So then A is all good. Now let's check D.
\[\bf x=-2\\y=3\\~\\12x - 3y = -33\]
i believe that D wouldn't work
What reason supports that belief?
Its really an educated guess
What is the "educated" in that educated guess?
So it's just a guess then
Here's a pro-tip for turning your guesses into certainty: \[\huge Do\\\huge the\\\huge work\]
\[\bf x=-2\\y=3\\~\\12x - 3y = -33\]
ok sorry im told I got to get off but I think its A am i right?
Well D is right too but yes, A is correct
Ok thanks alot
have a good night
U too, nite