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4 years ago

10 points all wrong answers will be reported and explain Solve using linear combinations show your work.

Mathematics

1 answer:

allochka39001 [22]4 years ago

3 0

Answer:

x = -5, y = 4, z = 3

Step-by-step explanation:

(1) 3x + y + 3z = -2

(2) 6x + 2y + 9z = 5

(3) -2x - y - z = 3

Step 1. Eliminate one of the variables in two of the equations

6x + 2y + 9z = 5 Subtract twice Equation (1)

6x + 2y + 6z = -4 from Equation (2)

3z = 9

z = 3

Step 2. Set up two new equations in two variables

3x + y + 9 = -2 Substitute z

-2x - y - 3 = 3 into (1) and (3)

(4) 3x + y = -11 Add Equations

(5) -2x - y = 6 (4) and (5)

x = -5

Step 3. Substitute x and z into one of the original equations

Substitute into (3)

-2(-5) - y - 3 = 3

10 - y - 3 = 3

7 - y = 3

- y = -4

y = 4

The solutions are x = -5, y = 4, z = 3.

Check:

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

-15 + 4 + 9 = -2

-2 = -2

(2) 6(-5) + 2(4) + 9(3) = 5

-30 + 8 + 27 = 5

5 = 5

(3) -2(-5) - 4 - 3 = 3

10 - 4 - 3 = 3

3 = 3

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