Question

Hi, I need help understanding how to solve this 3x3 System of Equations by elimination:
4x + 4y + z=24
2x - 4y + z = 0
5x - 4y - 5z = 12
I already know the values for each variable, I just want to know how to solve it myself

Answer 1

Does it has to be by elimination?

Answer 2

Yes please, the test will only have elimination problems and Cramer's rule. I already know how to use the latter

Answer 3

Sorry, I don't like elimination :c

Answer 4

All good

Answer 5

4x+4y+z=24 (1)
2x-4y+z=0 (2)
5x-4y-5z= 12 (3)
add (1) and (2)
6x+2z=24
3x+z=12 (4)
add (1) and (3)
9x-4z=36 (5)
multiply (4) by 4 and add in (5)
21x=48+36=84
x=84/21=4
put in (4)
3*4+z=12
z=12-12=0
put in (2)
2*4-4y+0=0
8=4y
y=8/4=2

Answer 6

In the calculator I used, I got y = -4 and z = 5

Answer 7

let us check the solution
put x=4,y=2 z=0 in any equation say (3)
5*4-4*2-5*0=12
20-8=12
or 12=12
which is true.

Answer 8

Ah, cool. Thanks so much!

Answer 9

yw