Question

Solve Three-Variable system by substitution ALGEBRA 2
5x-y+z=4 x+2y-z=5 2x+3y-3z=5

Answer 1

Start with one equation and solve for a variable, then substitute that variable into the second equation and solve for a second unknown, then substitute into the third equation and solve.

Answer 2

from 5x - y + z = 4 ==> z = 4 - 5x + y (*)
sub (*) into second equation, you got :
x + 2y - (4 - 5x + y) = 5
x + 2y -4 + 5x - y = 5 ==> 6x + y = 9 (**)
sub (*) into third equation, you got :
2x + 3y - 3(4 - 5x + y) = 5
2x + 3y - 12 + 15x -3y = 5 ==> 17x = 17 ==> x = 1

sub x = 1 into (**), you got:
6(1) + y = 9 ==> y = 3

sub bot x = 1, y = 3 into one of the original equation (say first one), you got

5(1) - 3 + z = 4 ==> z = 2

answer : x = 1, y = 3, z = 2
use this answer to check with second equation and third equation to make sure they are right.