Question

What is the solution of the system of equations?
{3x+2y+z=7}
{5x+5y+4z=3}
{3x+2y+3z=1}

Answer 1

Do you know the matrix method of solving such linear equations ?

Answer 2

@yelahn you there ?

Answer 3

i didnt think i had to use a matrix method. it just says to solve the system...

Answer 4

Its okay.

Answer 5

Lets solve it in a very easy way

Answer 6

okay. where do i start?

Answer 7

First of all select any two equations.

Answer 8

euation 1 &2

Answer 9

Ok

Answer 10

do i add the two equations or subtract??

Answer 11

That now depends.

From these 2 equations you have to remove at least one variable by solving them.

Answer 12

soo remove x?

Answer 13

Okay

Answer 14

Now, you can see that the coefficient of x in eq. 1 and 2 are not the same.

So, we are going to multiply eq. 1 and 2 by numbers such that the coefficients of x will become same.

Answer 15

For example:

If I multiply eq. 1 by 5 on both sides and eq. 2 by 3 on both sides, both will have 15 x. Right ?

Answer 16

right

Answer 17

what do you mean by both sides??

Answer 18

I meant multiply 5 in LHS and in RHS

Answer 19

woahhh slow down. whats LHS and RHS

Answer 20

LHS = left hand side of = sign

RHS = right hand side of = sign

Answer 21

so the equations would be
15x+2y+z=35
15x+5y+4z=15
???

Answer 22

Did you multiply 5 by 2y and z in eq. 1?

Answer 23

no

Answer 24

What I meant by multiplying 5 on both sides is this:

(3x+2y+z) = 7

=> 5*(3x+2y+z) = 5*7

Answer 25

okay so
15x+10y+5z=35

Answer 26

Yes

Answer 27

and eq2 is
15x+15y+12z=9

Answer 28

Very nice

Answer 29

and then 15x cancels out?

Answer 30

Yes subtract both equations and 15x would cancel out.

Answer 31

-5y+-7z=26

Answer 32

Yelahn, this : -+ or +- is not correct in maths, use instead -(+) or +(-). Ok?

-5y + (-7x) = 26 okay ?

Answer 33

oh. my mistake. i meant-5y-7z=26

Answer 34

Its ok

Answer 35

now what do i do

Answer 36

Now, you are going to find out the value of y in terms of z from this equation.

Answer 37

how/ thats seems impossible

Answer 38

See:

You had this equation:

-5y - 7z = 26

=> -5y = 26 + 7z

=> 5y = -26 - 7z

=> y = 1/5 * (-26-7z)

Answer 39

Did you get it ?

Answer 40

no i cant figure it out

Answer 41

Which step ?

Answer 42

y=1/5*(-26-7z)

Answer 43

What I did was that I divided by 5 on both sides . Ok ?

Answer 44

i got
y=-5.2-1.4z

Answer 45

Correct

Answer 46

Now, similarly select any other pair of equations.

Answer 47

should this one be simplified more? how can y=-5.2-1.4z

Answer 48

y=-6.6

Answer 49

How ?

Answer 50

no nvm. ignore that

Answer 51

k

Answer 52

So, now select any other pair of equations.

Answer 53

2 and 3

Answer 54

Ok

Now from these equation eliminate x.

Answer 55

why are you eliminating x again

Answer 56

I am doing this because after eliminating x, I am going to ask you to derive another relationship between y and z and then equate this relationship to the previous one.

Answer 57

So first eliminate x from this pair of equations.