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32 votes
32 votes
X+2y+3z = 12
x-3y + 4z=27
-x+y+2z=7

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User Woodsy
by
2.9k points

1 Answer

19 votes
19 votes

Answer:

x=1

y=−2

z=5

(heres how i got the answer)

Explanation:

x+2y+3z=12

x−3y+4z=27

−x+y+2z=7

Solve x+2y+3z=12 for x.

x=−2y−3z+12

Substitute −2y−3z+12 for x in the second and third equation.

−2y−3z+12−3y+4z=27

−(−2y−3z+12)+y+2z=7

Solve equations for y and z respectively.

y=−3+

5

1

z

z=

5

19

5

3

y

Substitute −3+

5

1

z for y in the equation z=

5

19

5

3

y.

z=

5

19

5

3

(−3+

5

1

z)

Solve z=

5

19

5

3

(−3+

5

1

z) for z.

z=5

Substitute 5 for z in the equation y=−3+

5

1

z.

y=−3+

5

1

×5

Calculate y from y=−3+

5

1

×5.

y=−2

Substitute −2 for y and 5 for z in the equation x=−2y−3z+12.

x=−2(−2)−3×5+12

Calculate x from x=−2(−2)−3×5+12.

x=1

The system is now solved.

x=1

y=−2

z=5

User Auramo
by
3.0k points