I can't figure this math problem out?

Question

Please help me. I can't figure out this math problem. I have an idea, but I don't think its right at all!


w + x + y + z = 24
3w - 2x - 3y + 3z + -9
5w + 3x - 2y -2z = 4
2w + 4x + 4y - 5z = 22
Find x, y, w, and z.

Answer 1

The most intuitive way to answer is to use Gauss-Jordan elimination, as described below.


w + x + y + z = 24
3w + 3x + 3y + 3z = 72
3w - 2x - 3y + 3z = -9
5x + 6y= 81

w + x + y + z = 24
5w + 5x + 5y + 5z = 120
5w + 3x - 2y - 2z = 4
2x + 7y + 7z = 116

w + x + y + z = 24
2w + 2x + 2y + 2z = 48
2w + 4x + 4y - 5z = 22
-2x - 2y + 7z = 26

2x + 7y + 7z = 116
-2x - 2y + 7z = 26

4x + 9y = 90
5x + 6y= 81

20x + 45y = 450
20x + 24y = 324
21y = 126

y = 6

4x + 9y = 90
4x + 54= 90
4x = 36
x = 9

2x + 7y + 7z = 116
18 + 42 + 7z = 116
7z = 56
z = 8

w + x + y + z = 24
w + 9 + 6 + 8 = 24
w = 1
{w,x,y,z} = {1,9,6,8}

Another method is to put the coefficiants into a matrix, and put it into reduced-row echelon form.

|1 1 1 1 24|
|3 -2 -3 3 -9|
|5 3 -2 -2 4|
|2 4 4 -5 22|

In RREF...
|1 0 0 0 1|
|0 1 0 0 9|
|0 0 1 0 6|
|0 0 0 1 8|

These are all new valid equations, just in a much nicer form. Specially, 1w+0x+0y+0z=1, etc.
This tells us that w=1, x=9, y=6, and z=8.

Also, you could use Cramer's rule with these equations and get the same answer, but I will not demonstrate that one.

Answer 2

4 simultaneous equations and 4 variables. You solve them by first using 1 equation to eliminate all of one variable from the other 3. Then you are left with 3 simultaneous equations and 3 variables. Repeat the process with the remaining 3 equations to get 2 equations and 2 variable then one more time to get 1 equation and 1 variable. Solve for that 1 variable, then start plugging the answers back into the previous equation sets and solving for the variables.

This will take some time and you will need to be carefull that each step is done correctly. I am not going to do it for you.

Answer 3

on your case, you're a million/8 Irish and (something) 7/8 black. The fraction 7/8 is surely 87.5%. So saying you're 87% black (nevertheless surely it could around as much as 88%) is unquestionably comparable to saying 7/8 black. often, to make certain the ethnic possibilities or fractions of somebody, you upload up all of the fractions of the mummy and dad, in my opinion upload together any comparable ethnicities, and divide each little thing via 2. as an occasion, in my case my mom is one hundred% Irish and my father is 0.5 French and 0.5 Irish. So my ethnicity is: [ (one hundred% Irish) + (50% French + 50% Irish) ] / 2 = [ one hundred fifty% Irish + 50% French ] / 2 = (one hundred fifty/2)% Irish + (50/2)% French = 75% Irish + 25% French you're able to do an identical with fractions and land up with an identical outcomes (3/4 Irish, a million/4 French). it is on account which you often get 0.5 of your ethnicity out of your mom, and 0.5 out of your father. in addition, you ought to take 0.5 of their ethnicities, and then upload up the fractions. you will continuously get an identical outcomes the two way, by way of fact the approaches are algebraically equivalent. Getting decrease back on your loved ones. If we assume the 7/8 & a million/8 is genuine, and that your father is one hundred% black, then your mom could ought to be a million/4 Irish and 3/4 black. this form you get (a million/4 Irish + 3/4 black + a million/a million black) / 2 = (a million/4 Irish + 7/4 black)/2 = a million/8 Irish, 7/8 black. this could recommend that her mom (your maternal grandmother) is a million/2 Irish and a million/2 black. On a facet observe, there is surely no way you would be a million/3 of a few thing. If we assume that ancestors continuously hint decrease back to people of a few one hundred% ethnicity, and someone has 2 and in elementary terms 2 organic and organic mum and dad, then you definately can in elementary terms artwork in multiples of powers of a million/2. you won't be able to upload up halves, quarters, eighths, etc. and get thirds. EDIT: I initially wrote "African" for "black", no longer by way of fact i presumed I had to be %., yet by way of fact i presumed geography replaced into the defining element right here merely because it is for "Irish". yet then i found out that "black" can confer with ethnicities technically no longer from the continent and vice versa so I went with the extra generic term.

Answer 4

I agree with Math Avenger!