Question

Solve the system of linear equations and check any solution algebraically.
2x +2z = 6
5x +3y = 11
3y -4z = 1

Answer 1

You know about operations inside a matrix?

Answer 2

nope

Answer 3

also using elimination method.., do you know???

Answer 4

Try substracting line 3 to line 2, what does line 2 become?

Answer 5

hey get z in terms of x from 1st equation, y in terms of x from 2nd equation.
subtite both in third equation ,you will get a value for x. from then calculate z and y.

Answer 6

@theloser it can be done that way, but it'll probably be worth a 0 in an exam on Linear Algebra. They want to pave the way for more complicated problems using matrices.

Answer 7

Line 2 would become
5x+0+4z=10
Do you see what I've done?

Answer 8

@AlexUL i got -5x +3y = -10 but i clearly did something wrong

Answer 9

@AlexUL never mind i got that too now

Answer 10

2x +2z = 6 |x5|
5x +3y = 11 |x2|
--------------- -

10x +10z = 30
10x +6y = 22
-------------- -
10z - 6y = -2


-6y + 10z = -2 |x1|
3y -4z = 1 |x2|

-6y + 10z = -2
6y -8z = 2
-------------- +

0 + 2z = 0
z = 0

so

10z -6 = -2
0 -6y = -2
-6y = -2
y = 1/3


10x +6y = 22
10x + 6 (1/3) = 22
10x + 2 = 22
10x = 22-2
10x = 20
x = 2

Answer 11

ok, good! :P
Now, how can you simplify even more line 2, so you end up with only x or z?

Answer 12

x = 2
y = 1/3
z = 0

Answer 13

@gerryliyana the answer in the back of the book says (-2, 7, 5)

Answer 14

sorry i'm wrong

Answer 15

@gerryliyana it's okay :)

Answer 16

@AlexUL who said that have to be solved by matrices only. btw here the coeff' matrix will have 1 zero in all columns and rows. so the method i have told works better. if the coefficient matrix dint have any zeros, then taking inverse and all that stuff works better.

Answer 17

x=-2,y=7,z=5

Answer 18

@pkjha3105 how'd u do that?

Answer 19

i hv solvd in rough...doesnt it satisy the eq?

Answer 20

@pkjha3105 that's the correct answer but i wanna know how to solve it

Answer 21

rewrite 1st equation as z = 3-x
2nd as \[y = \frac{ 11-5x }{ 3 }\]

put and y and z values in third equation

Answer 22

solve by matrix methrd...put all constant in one 3 by 3 matrix,multiply it by matrix of varible and equate to matrix,wch contains the value of rhs....then find the inverse of matrix containg constant n multiply by rhs....u will get the value of x,y,z...

Answer 23

2x +2z = 6 |x5|
5x +3y = 11 |x2|
--------------- -

10x +10z = 30
10x +6y = 22
-------------- -
10z - 6y = 8

-6y + 10z = 8 |x1|
3y -4z = 1 |x2|

-6y + 10z = 8
6y -8z = 2
-------------- +
0 + 2z = 10
z = 10/2
z = 5


so
10z -6 = 8
10 (5) -6y = 8
-6y = 8 -50
y = -42/-6
y =7


5x +3y = 11
5x + 3(7) = 11
5x + 21 = 11
5x = 11-21
x = -10/5
x =-2

Answer 24

how about that @lawls ??

Answer 25

the answer is

x = -2
y = 7
z =5

take it easy.,

Answer 26

@theloser so 3((11-5x)/3) - 4(3-x) = 1

Answer 27

heiii @lawls
look at my LAST solution!

Answer 28

@gerryliyana good job u got the answer. i'm gonna see how u did it now.

Answer 29

@lawls thank you :)

Answer 30

@theloser
The question says "check any answer algebraically", I think this means you have to find the answer in another way, and if lawls is studying systems of linear equations and has written the system as a matrix, I assume you need to work it out with matrices operations

Answer 31

@lawls .. exactly, from that you will get x= -2, subtitute in z and y exprestion which are in terms of x...

Answer 32

@AlexUL , no check answer algebraically , i think would mean, keep the point in all there equations. and if it is correct i will satisfy them

Answer 33

it is preferable to solve these eq. by matrix methord only....find the inverse of matrix containing const. and multiply by the matrix of rhs....x,y,z...can easily b found by this methord...

Answer 34

@pkjha3105 & @AlexUL my teacher hasn't taught us about matrices yet. in class he solved these types of questions in @gerryliyana way so i'm gonna use that, but thanks so much though.

Answer 35

@theloser i got the answer in your way as well. it was very simple. thanks :)

Answer 36

ur welcome @lawls
good job! :)