What am I doing wrong? Solving for three unkowns?

Question

I am doing my homework but this one problem I've done 3 times always comes out wrong.

3x-5y+z=8
4y-z=10
7x+y=4

I get y= -11.4
x=2.2
z=55.6

I know I'am doing it wrong but what am I doing wrong?

Answer 1

You're doing nothing wrong. That is in fact the correct answer.

Edit: oh wait, you said z=55.6 . That is wrong, it should be z= -55.6 . You probably made a sign error somewhere.

Answer 2

You can easily put this problem into a scientific calculator and solve this. I am sure that is not what you are trying to do, but if you know how do use matrices, this equations becomes a little bit easier.

First, in your calculator, go to the MATRIX function. Enter in your system of equations as a matrix. This will look like:

3 -5 1 8
0 4 -1 10
7 1 0 4

Then, also using your calculator, put this function into Reduced Row Echelon Form (to use this on my calculator, the symbol for the reduced row echelon form is rref). This will show up like this:

1 0 0 .3
0 1 0 1.9
0 0 1 -2.4

meaning, x=.3, y=1.9, and z=-2.4

You can do this by hand too. Starting with your matrix, start moving things around to make the first number (where the 3 currently is) 1. Then, make the other numbers below that 1 zero by adding or subtracting a constant or even another row. Continue doing this until you have your matrix in the form of

1 0 0 x
0 1 0 y
0 0 1 z

Where x,y, and z are whatever constants you get at the end.

A quick search of Reduced Row Echelon Form would probably explain this better than I can.

Good Luck!

Answer 3

z should be negative

3x - 5y + z = 8
4y - z = 10
7x + y = 4

4y - z = 10
4y = z + 10
y = (1/4)z + (5/2)

7x + y = 4
7x + ((1/4)z + (5/2)) = 4
7x + ((1/4)z + (10/4)) = 4
7x + (1/4)(z + 10) = 4
28x + (z + 10) = 16
28x + z + 10 = 16
28x = -z + 6
x = (-1/28)z + (3/14)

3x - 5y + z = 8
3((-1/28)z + (3/14)) - 5((1/4)z + (5/2)) + z = 8
(3/28)(-z + 6) - 5((7/28)z + (70/28)) + z = 8
(3/28)(-z + 6) - (35/28)(z + 10) + z = 8

Multiply everything by 28

3(-z + 6) - 35(z + 10) + 28z = 224
-3z + 18 - 35z - 350 + 28z = 224
(-3 - 35 + 28)z + (18 - 350) = 224
-10z - 332 = 224
-10z = 556
z = (-556/10)
z = (-278/5)

x = (-1/28)z + (3/14)
x = (-1/28)(-278/5) + (3/14)
x = (278/140) + (3/14)
x = (139/70) + (3/14)
x = (139/70) + (15/70)
x = (139 + 15)/70
x = (154/70)
x = (11/5)

y = (1/4)z + (5/2)
y = (1/4)(-278/5) + (5/2)
y = (-278/20) + (5/2)
y = (-139/10) + (5/2)
y = (-139/10) + (25/10)
y = (-139 + 25)/10
y = (-114/10)
y = (-57/5)

so

x = (11/5) or 2.2
y = (-57/5) or -11.4
z = (-278/5) or -55.6

Answer 4

3x-5y+z=8
4y-z=10
7x+y=4

Step One;
well dear first just get 2 functions together
4y-z=10
7x+y=4

multiply '-4' to the second function ,
-4 * ( 7x+y=4)
-28 x- 4y = -16

Step Two;
so lets carry on ;
4y - z = 10
-28 x - 4y = -16
__________________
- 28 x - z = -6 { its the new function.}

- 28 x - z = -6
3x - 5y +z = 8 { here u can remove z }
so we have ;
-25x - 5y = +2 { anouther function }

Step Three;
-25x - 5y =+2
7x + y = 4
{ multiply the second function by ' +5 ' }
+5 * ( 7x + y = 4 ) = 35x + 5y = 20
so we have;
- 25 x - 5y = +2
35x + 5y = 20
_________________
10x = 22
x = 22/10
x = 2.2

Step Four;
now just substitute the value of x in one of the functions.
7(2.2) + y = 4
15.4 + y = 4
y = 4 - 15.4
y = - 11.4

Step Five;
now z;
4y - z = 10
4(-11.4) - z =10
- 45.6 - 10 = z
z = - 55.6

well dear you got all correct except z u just forgot to put ' - ' before the value of z . congratulation , great job.
Good Luck.

Answer 5

You can use substitution. The way the equations are give is set up for it. Solve for z in the second equation and y in the last equation.
you get: z = 4y+10 and y = -7x+4
plug the z equation into the first eq. You get
3x-5y+4y+10=8 That solves to 3x-y = -2
then plug in the y eq.
you get: 3x+7x-4 = -2. That simplifies to 10x = 2.
x = 1/5
Now use that to find y and the value of y to find z.
These problems always seem to have crazy fraction answers.

the answers should be x = 1/5, y = 13/5, z = 102/5
Don't do anything to the fractions, most teachers will want them in this form.

Answer 6

3x-5y+z=8
4y-z=10
7x+y=4

y = 4 - 7x

z = 4y - 10

x = 4 -y /7

put it all in the first one.

Answer 7

Jim can fill a pool donning greenbacks of water in half-hour. Sue can do the comparable job in 40 5 minutes. Tony can do the comparable job in a million ½ hours. How right now can all 3 fill the pool mutually? Jim = a million/2 guy-hr Sue = 3/4 guy-hr Tony = a million.5 guy hr enable x = the completed volume of paintings to be performed in my view

Answer 8

Your answer is absolutely right except for the Z= - 55.6 !
if you really doubt it , check your equations again and see ..
But for you for your answer to match these equations you can solve these equation with your resulted answers look :

3X-5Y+Z= 8 __________(1)

Now lets see if it equals = 8

3*2.2 - 5*(- 11.4 ) + ( - 55.6) = ?

6.6 + 57 - 55.6 = 8 _________________(1)

4Y - Z = 10 __________(2)

(4* -11.4 ) - ( - 55.6 ) = ?

45.6 + 55.6 = 10 _____ (2)

And so does the third , so your solutions satisfy your equations

Answer 9

3x-5y+z=8

I think that substitution to get all y's would work good here

4y-z=10
z=4y-10

7x+y=4
7x=4-y
x=4/7-y/7

3(4/7-y/7)-5y+4y-10=8
12/7-3y/7-5y+4y-10=8
12-3y-35y+28y-70=56
-10y-58=56
-10y=114
y=-11.4

looks like I got the same number as you

why do you think its wrong?

perhaps you just need to express it as a fraction

y=-11.4=-11 4/10=-11 2/5=-57/5

or maybe we both made the same mistake
guess I'll have to see what others came up with

Answer 10

Isolate z in number 2 and y in number 3 and put the new equations in the first instead of y and z. Then it will be 3x-5*(4-7x)+(4*(4-7x)-10)=8 then solve x. Then you can easily find y in the 3rd equation and find z in the 2nd...

Thomas