Question

help!!!
5x+7y=-1
-2y+3z=9
7x-z=27

Answer 1

x=4
y=-3
z=1

Answer 2

you used rref ?

Answer 3

okay..i need to know how to do them...

Answer 4

wats rref..this is scaring me...

Answer 5

techno how did you solve it

Answer 6

rref? i don't know what he means by that.
But the answer will be...x=4 y=-3 and z=1

Answer 7

how did you solve it

Answer 8

okay...but how?

Answer 9

plz dunt say "i dunt noe? i used mental math"

Answer 10

First work on an equation to solve, and then you plug in a variable and you plug it back for the other equation.

Answer 11

but whadda bout in this case..wad do i do first? and hw did u do it so fast?

Answer 12

I got an A in it...it's simple.

Answer 13

ughh..dunt say its simple...i suck at it and i got a C- in alg 2 rite now...

Answer 14

ok lets use strategy

Answer 15

lol ok

Answer 16

yes plz..i really need a stragety...to do dis problem and the other zillion

Answer 17

the two main strategies are elimination and substitution

Answer 18

okay...

Answer 19

substitution might be faster here, dunno.
we can do both ways. ok for elimination we want it to look like this first

Answer 20

go on...

Answer 21

5x+7y + 0z = -1
0x -2y+3z = 9
7x+0y -z = 27

Answer 22

okay....

Answer 23

wat next?

Answer 24

lets call them equation 1, 2, 3, .
the general strategy is , eliminate x from equation 1 and 2 , (using their lcm)
then eliminate x from equations 1 and 3 (using lcm and subtracting each other )

Answer 25

that leaves you with two equations in two unknowns ( y and z )

Answer 26

ohhh...i was so confused about the missing x in one of the equations...LOL

Answer 27

so equation 1 and 2 are
5x+7y + 0z = -1
0x -2y+3z = 9
unfortunately we cant eliminate x here though because second equation has a 0 in front of x

Answer 28

so lets eliminate x from equations 1 and 3 , you follow so far>

Answer 29

so we can skip the first step

Answer 30

kk.im following...

Answer 31

we will eliminate x from equation 1 and 3 :
5x+7y + 0z = -1
7x+0y -z = 27

Answer 32

the lcm is 35 , so multiply each other by the missing factor

Answer 33

kk

Answer 34

(7)(5x+7y + 0z) = (-1)(7)
-5(7x+0y -z) = (27)

Answer 35

leaving with
35x+49y+5z=-7
-35-5y-5z=-135

Answer 36

(7)(5x+7y + 0z) = (-1)(7)
-5(7x+0y -z) = -5
(27)

Answer 37

i used -5 because then we can just add

Answer 38

35 x + 49 y + 0z = -7
-35 x + 0y +5xz = -27*5

Answer 39

me too...

Answer 40

how is it 5xz thou?

Answer 41

typo

Answer 42

oh...

Answer 43

isnt it also 5y thou?

Answer 44

yes typo

Answer 45

lol..i thought i was wrong...

Answer 46

35 x + 49 y + 0z = -7
-35 x + 0y +5z = -27*5

Answer 47

but wait..isnt it also 5y?

Answer 48

oh wait...nevermind...

Answer 49

ok i added them and got
49y + 5z = (-7 - 135)

Answer 50

now wad do i do?

Answer 51

now you have two equations in y and z

Answer 52

49 y + 5z = -142
-2y + 3z = 9

Answer 53

so u eliminate one of the variables wit tat equation and the second one?

Answer 54

yes, you can now eliminate z or y

Answer 55

im thinking the z's rite..cuz tay are smaller numbers

Answer 56

it looks easier to eliminate z because lcm of 5 and 3 is 15

Answer 57

yea...

Answer 58

so once you find what y is, you back substitute

Answer 59

but wait tat cant work....

Answer 60

Here's how to do it using elimination. Ugly numbers...but you get the right answer:

This is how to do elimination. It's very methodical, so you have less
of a chance getting confused.

5x+7y=-1
-2y+3z=9
7x-z=27

rewrite, using only the coefficients
(always in the order x y z)
5 7 0 -1
0 -2 3 9
7 0 -1 27

Now make all the numbers below 5 zero,
by multiplying the top row by a number
and adding to the row. Here row 2 already has a zero.
For row 3, multiply the top row by -7/5 and add to row3.
(We pick -7/5 because -7/5 times the 5 in the first row= -7
and -7 +7 in the 3rd row is zero)

Here -7/5*(5 7 0 -1 )= (-7 -9.8 0 1.4)

5 7 0 -1 <-- leave alone
0 -2 3 9 <-- leave alone
7 0 -1 27 <-- add (-7 -9.8 0 1.4) (comes from -7/5 times 1st row)

5 7 0 -1
0 -2 3 9
0 -9.8 -1 28.4

now use the 2nd row, 2nd number, and make everything below it zero
so multiply the 2nd row by -9.8/2 = -4.9. We get
-4.9*(0 -2 3 9)= (0 9.8 -14.7 -44.1)
5 7 0 -1 <-- leave alone
0 -2 3 9 <-- leave alone
0 -9.8 -1 28.4 <-- add (0 9.8 -14.7 -44.1)

5 7 0 -1 <-- leave alone
0 -2 3 9 <-- leave alone
0 0 -15.7 -15.7

Now back substitute:
the last line means -15.7z= -15.7, and z= 1

the 2nd line means -2y + 3z= 9
with z=1, we find y= -3

Finally, 5x+7y= -1, with y= -3, we have x= 4

Answer 61

wow...

Answer 62

wat a long reply...its been an hour...