T Nation

Math Help?


#1

Hi everyone havent done maths since highschool(in third year uni) and am quite stuck on this one problem, I'm probably doing just one thing wrong but cant figure it out

Solve the following linear simultaneous equation systems for y and x.

(a) y = 8x + 4 ; 3y = 2x â?? 6

it would be appreciated if someone could lend a hand

cheers


#2

Knowing what symbol the a?? mark thing is would help.


#3

oh shit forgot this website doesnt like copying things across

3y=2x-6 is the right side of the equation


#4

well its easy just put "8x+4" instead of "y" in the second equation ..resolve it that way and then resovle teh first one with teh info gathered..or just give me what a?? is and ill do it for u


#5

OK there are a few ways to solve this. Substitution may be the easiest. if y = 8x + 4 and 3y = 2x "something" 6
we can multiply the left equation by 3. so it becomes 3*y = (3*8)x + (3*4) or for simplicity 3y = 24x + 12 so if we have the other equation we get to replace things. if 3y = 24x +12 and 3y = 2x "something" 6. we can set the two things equal
24x + 12 = 2x "something" 6 so then just solve from there.
Hope that helps. post or PM if you have any other questions or if you need more explanation.


#6

thanks everyone it clicked the subsitution part as soon as i posted the next part....


#7

y = 8x + 4
3y=2x-6

24x+12=2x-6
24x-2x=-6-12
22x=-18
x=-18:22

y=8 -18:22 +4
y=-144:22 +4
well i think ive done it right but its 4 am in here and i cant think properly..Ill have look at it tomorrow..


#8

answers were x = -9/11 and y= -28/11


#9

edit: I don't know how to make it nice and neat so i just gave everything it's own line for the sake of it.

This is the simplest way to solve it:

y = 8x +4 -A
3y = 2x -6 -B

multiply A by 3 and subtract B from A.

3y = 24x + 12
- (3y= 2x - 6)


0y = 22x + 18 (its 12 MINUS MINUS 6 which is the same as 12 + 6 )

So now 0 = 22x +18
-18 = 22x
-18/22 = x
You can simplify by dividing both 18 and 22 by 2

which gives
-9/11 = x

Then to get y you just plug back in your value of x.
You can pick either y formula given but i'll do both for the sake of completion.

A: y = 8x +4 =>

y = 8(-9/11) + 4
= -72/11 + 4
= -72/11 + 4 * 1
= -72/11 + 4 * (11/11 = 1)

= -72/11 + 44/11

               y = -28/11

B: 3y = 2x -6 =>

3y = 2(-9/11) -6
= (-18/11) - (6 times 1 = 6)
= (-18/11) - (6 times 11/11 = 6)
= (-18/11) - 66/11 = -84/11

     3y = -84/11
      y = (-84/11)/3

= (-84/1) times (1/11) times (1/3) --- (you can rearrange it however you like it doesn't matter)
= (-84/3)/11
= -28/11

So,
x is -9/11
y is -28/11

If you don't get anything write it out on paper. Doing the problem/solution yourself is usually more helpful in making you understand it than doing mental mathematics, even if you're just copying it. As long as you try to understand it as you rewrite it, you'll get it.


#10

3y = 2x-6
y = 8x + 4
3(8x + 4) = 2x-6
24x + 12 = 2x - 6
22x = -18
x = -9/11

plug in x

y = 8*(-9/11) + 4 = -(72)/11 + (4*11)/11 = -28/11