Question

How do you do this linear system?

{3x+y+2z=3
X-2y+3z=1
4x-8y+12z=7

Answer 1

is it matrices or which topic

Answer 2

Look at equation 1 where you see the term 1y or just y

isolate that y to get

3x+y+2z=3

y=3-3x-2z

Answer 3

now go to the other 2 equations and replace y with 3-3x-2z

Answer 4

let @jim_thompson5910 take care of that

Answer 5

so equation 2 goes from

x-2y+3z=1

to

x-2(3-3x-2z)+3z=1

x-6+6x+4z+3z = 1

7x-6+7z = 1

7x+7z = 1+6

7x+7z = 7

7(x+z) = 7

7(x+z)/7 = 7/7

x+z = 1

Answer 6

oh my

Answer 7

Now focus on Equation 3

4x-8y+12z=7

4x-8(3-3x-2z)+12z=7

4x-24+24x+16z+12z=7

28x-24+28z=7

28x+28z=7+24

28x+28z=31

Answer 8

After doing all that, things boil down to these 2 equations

x+z = 1
28x+28z=31

Answer 9

use any method to solve that new system of equations for x and z

once you have x and z, you can use them both to find y