1. Let's solve for x.
x−2y−z=−6
Step 1: Add 2y to both sides.
x−2y−z+2y=−6+2y
x−z=2y−6
Step 2: Add z to both sides.
x−z+z=2y−6+z
x=2y+z−6
Let's solve for y.
x−2y−z=−6
Step 1: Add -x to both sides.
x−2y−z+−x=−6+−x
−2y−z=−x−6
Step 2: Add z to both sides.
−2y−z+z=−x−6+z
−2y=−x+z−6
Step 3: Divide both sides by -2.
−2y
−2
=
−x+z−6
−2
y=
1
2
x+
−1
2
z+3
Let's solve for z.
x−2y−z=−6
Step 1: Add -x to both sides.
x−2y−z+−x=−6+−x
−2y−z=−x−6
Step 2: Add 2y to both sides.
−2y−z+2y=−x−6+2y
−z=−x+2y−6
Step 3: Divide both sides by -1.
−z
−1
=
−x+2y−6
−1
z=x−2y+6
2.Let's solve for x.
−x+6y−3z=18
Step 1: Add -6y to both sides.
−x+6y−3z+−6y=18+−6y
−x−3z=−6y+18
Step 2: Add 3z to both sides.
−x−3z+3z=−6y+18+3z
−x=−6y+3z+18
Step 3: Divide both sides by -1.
−x
−1
=
−6y+3z+18
−1
x=6y−3z−18
Let's solve for y.
−x+6y−3z=18
Step 1: Add x to both sides.
−x+6y−3z+x=18+x
6y−3z=x+18
Step 2: Add 3z to both sides.
6y−3z+3z=x+18+3z
6y=x+3z+18
Step 3: Divide both sides by 6.
6y
6
=
x+3z+18
6
y=
1
6
x+
1
2
z+3
Let's solve for z.
−x+6y−3z=18
Step 1: Add x to both sides.
−x+6y−3z+x=18+x
6y−3z=x+18
Step 2: Add -6y to both sides.
6y−3z+−6y=x+18+−6y
−3z=x−6y+18
Step 3: Divide both sides by -3.
−3z
−3
=
x−6y+18
−3
z=
−1
3
x+2y−6
Let's solve for x.
2x−11y+5z=−33
Step 1: Add 11y to both sides.
2x−11y+5z+11y=−33+11y
2x+5z=11y−33
Step 2: Add -5z to both sides.
2x+5z+−5z=11y−33+−5z
2x=11y−5z−33
Step 3: Divide both sides by 2.
2x
2
=
11y−5z−33
2
x=
11
2
y+
−5
2
z+
−33
2
Let's solve for y.
2x−11y+5z=−33
Step 1: Add -2x to both sides.
2x−11y+5z+−2x=−33+−2x
−11y+5z=−2x−33
Step 2: Add -5z to both sides.
−11y+5z+−5z=−2x−33+−5z
−11y=−2x−5z−33
Step 3: Divide both sides by -11.
−11y
−11
=
−2x−5z−33
−11
y=
2
11
x+
5
11
z+3
Let's solve for z.
2x−11y+5z=−33
Step 1: Add -2x to both sides.
2x−11y+5z+−2x=−33+−2x
−11y+5z=−2x−33
Step 2: Add 11y to both sides.
−11y+5z+11y=−2x−33+11y
5z=−2x+11y−33
Step 3: Divide both sides by 5.
5z
5
=
−2x+11y−33
5
z=
−2
5
x+
11
5
y+
−33
5
the spaces r meant to be fractions