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2 votes
Solve the system of equations.
x - 2y- z = -6
-x+6y-3z = 18
2x−11y+5z = -33

User M Brown
by
4.9k points

1 Answer

3 votes

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

User SamwellTarly
by
5.7k points