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# simultaneous equation help Watch

1. The question is

3x-4y=4
9x-7y=22

so I multiplied the first equation by 7 and second by 4 so they both give the same value for the middle bit which is 28.

After that I don't understand.
2. (Original post by z_o_e)
The question is

3x-4y=4
9x-7y=22

so I multiplied the first equation by 7 and second by 4 so they both give the same value for the middle bit which is 28.

After that I don't understand.
Well, subtract the two equations from one another?
3. So you have -28y in the first equation and -28y in the second. Try taking (the new first equation) from (the new second equation).
4. (Original post by z_o_e)
The question is

3x-4y=4
9x-7y=22

so I multiplied the first equation by 7 and second by 4 so they both give the same value for the middle bit which is 28.

After that I don't understand.
another quicker way is to multiply

3x-4y=4 by 3 then takeaway the equation from each other
5. (Original post by Math12345)
So you have -28y in the first equation and -28y in the second. Try taking (the new first equation) from (the new second equation).
What do you mean?

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6. 1. 3x-4y=4
2. 9x-7y=22

It may be easier for you to deal with the 'x'

3. 9x - 12y = 12 (multiplied by 3)
4. 9x - 7y = 22 (kept the same)

Subtract the second equation from the first, removing the 9x

-5y = 10

Divide both sides by -5 to get y on its own.
y = 2

Substitute y = -2 (SOLVE)

3x - 4(2) = 4
3x - 8 = 4
3x = 12
x = 4
7. (okay well someone else wrote an answer as well but i was writing mine and i don't want my work to go to waste so i'll just post it okay)

3x-4y=4
9x-7y=22

Well, the first thing you need to keep in mind is that, based on what is easiest, either the x's or y's should be comprised of the same number, except on negative and one positive. (or both the same if you'll subtract the equations instead)

In this case, it'd be easier to just multiply the first equation by -3. Saves time and smaller numbers.

So:

-9x+12y=-12
9x-7y=22

So, heres the thing, we add up the equations. (Why? Because logically speaking, if -9x+12y=-12 and 9x-7y=22, then -9x+9x+12y-7y=-12+22 )

So basically: (see spoiler)
Spoiler:
Show
I added -9x+(+9x) to give 0. This was why we multiplied, so that we could eliminate one of the variables.

Then +12y+(-7y) to give +5y. Then, then last one is explanatory.

Now that you know y, substitute it in any of the original equations and get x.
Then test both x and y in the remaining equation to make sure it gives the same end result.

(p.s I know I did a slightly more complicated route, but that's what I was used to. I can't believe I never thought of the subtract method before. That's my whole life lived like this. What a life it was)
8. (Original post by shaafay)
(okay well someone else wrote an answer as well but i was writing mine and i don't want my work to go to waste so i'll just post it okay)

3x-4y=4
9x-7y=22

Well, the first thing you need to keep in mind is that, based on what is easiest, either the x's or y's should be comprised of the same number, except on negative and one positive. (or both the same if you'll subtract the equations instead)

In this case, it'd be easier to just multiply the first equation by -3. Saves time and smaller numbers.

So:

-9x+12y=-12
9x-7y=22

So, heres the thing, we add up the equations. (Why? Because logically speaking, if -9x+12y=-12 and 9x-7y=22, then -9x+9x+12y-7y=-12+22 )

So basically: (see spoiler)
Spoiler:
Show
I added -9x+(+9x) to give 0. This was why we multiplied, so that we could eliminate one of the variables.

Then +12y+(-7y) to give +5y. Then, then last one is explanatory.

Now that you know y, substitute it in any of the original equations and get x.
Then test both x and y in the remaining equation to make sure it gives the same end result.

(p.s I know I did a slightly more complicated route, but that's what I was used to. I can't believe I never thought of the subtract method before. That's my whole life lived like this. What a life it was)
Omg thank you so much! This is so helpful!
So X is 4.
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9. 3x-4y=4 ---> 3x = 4 + 4y ----> x = 4/3 + 4y/3 ----> sub in x for 9x-7y=22 ----> 9(4/3 + 4y/3)-7y=22 ---> now you can work out y
9x-7y=22
10. (Original post by SalazarSlytherin)
3x-4y=4 ---> 3x = 4 + 4y ----> x = 4/3 + 4y/3 ----> sub in x for 9x-7y=22 ----> 9(4/3 + 4y/3)-7y=22 ---> now you can work out y
9x-7y=22
What am I doing wrong in this question? :/

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11. (Original post by z_o_e)
What am I doing wrong in this question? :/

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I think it's because you forgot to multiply 18 by 5 lol
12. (Original post by z_o_e)
What am I doing wrong in this question? :/

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I dont know what you are doing on that piece of paper but I have solved it for you. Any questions ask me

https://gyazo.com/183b917826e6a77a35fe53e0fb06d973
13. (Original post by shaafay)
I think it's because you forgot to multiply 18 by 5 lol
Oh lol thank you X

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14. (Original post by z_o_e)
Oh lol thank you X

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haha, no problem. we've all suffered from silly little mistakes :3
15. (Original post by shaafay)
haha, no problem. we've all suffered from silly little mistakes :3
This seems wrong :/

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16. (Original post by z_o_e)
This seems wrong :/

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You've probably figured this out by now, but you made a mistake adding 240 and -370. You accidentally did 240+370, not 240+(-370). It should be -130, not 610.

Remember to always keep the signs in check :3

(I got x=-2 btw)
17. (Original post by shaafay)
You've probably figured this out by now, but you made a mistake adding 240 and -370. You accidentally did 240+370, not 240+(-370). It should be -130, not 610.

Remember to always keep the signs in check :3

(I got x=-2 btw)
Got it thank you so much

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