−2x + 3y + 5z = −21
−4z = 20
6x − 3y = 0
do -4z=20 first
divide both sides by -4 to get z by itself
-4z/-4=20/-4
z=-5
Use z=-5 into −2x + 3y + 5z = −21
-2x+3y+5(-5)=-21
-2x+3y-25=-21
move -25 to the other side
sign changes from -25 to +25
-2x+3y-25+25=-21+25
-2x+3y=4
6x-3y=0
find x by eliminating y
Add the equations together
-2x+6x+3y+(-3y)=4+0
-2x+6x+3y-3y=4
4x=4
Divide by 4 for both sides
4x/4=4/4
x=1
Use x=1 into 6x − 3y = 0
6(1)-3y=0
6-3y=0
Move 6 to the other side
6-6-3y=0-6
-3y=-6
Divide both sides by -3
-3y/-3=-6/-3
y=2
Answer:
(1, 2, -5)