Question

Systems of Equations, please help =)

Solve without matrix
5x-y+z=4; x+2y-2=5; 2x+3y-3=5

I have the answer, but have tried multiple times and cannot get to it.

Answer 1

WAIT that's the wrong equation!!
It's
5x-y+Z=4, x+2y-Z=5, 2x+3y+3Z=5

Answer 2

so which letter do you want to eliminate... y or z..?

Answer 3

Whichever is easier.

Answer 4

ok... so we'll eliminate z you'll end up with 2 equations in 2 unknowns

so add equations 1 and 2

5x -y + z = 4
x + 2y - z = 5
--------------
6x + y = 9 equation 4

now multiply equation 2 by 3 and add equation 3

3x + 6y -3z = 15
2x + 3y + 3z = 5
-----------------
5x + 9y = 20 equation 5


easiest thing to do now is to multiply equation 4 by 9 and subtract equation 5 which will eliminate y

54x + 9y = 81
- 5x - 9y = -20
--------------
49x = 61

Answer 5

you'll need to check the calculations

Answer 6

So x=(61/49)?

Answer 7

the unlucky thing about the question you posted is that the answers are all ugly fractions...

but I hope it helps

you should be able to get x

then substitute it into either equation 4 or 5 to find y

then substitute the values of x and y into any of the original equations to find x

hope it makes sense

Answer 8

that's x... very ugly

Answer 9

Huh. The answer is x=1, y=3, z=2...

Answer 10

well you need to check the equations

1st seems ok... 5 - 3 + 2 = 4

2nd 1 + 6 - 2 = 5

3rd 2 + 9 + 6 = 17 you have 5

can you check the 3rd equation in the repost....

Answer 11

so it looks like the last equation should be

2x + 3y - 3z = 5

Answer 12

Yes. Oops!! So sorry

Answer 13

ok... so equation 4 is fine...

now multiply equation 1 by 3 and then add equation 3\\

15x - 3y + 3z = 12
2x + 3y + 3z = 5
------------------
17x = 17

so now that makes sense...

find x, substitute it into equation 4 to find y

then substitute the values into any of the original equations to find z

hope it now makes sense.

Answer 14

oops should read -3z = 5

Answer 15

yes!! thank you so much!!