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VARVARA [1.3K]
3 years ago
13

Given the system of equations 2 x − 3 y − 9 z = 9 x + 3 z = 3 − 3 x + y − 4 z = − 10 (a) determine whether the system is inconsi

stent or dependent; Your answer is (input inconsistent or dependent) dependent Correct (b) if your answer is dependent in (a), find the complete solution. Write x and y as functions of z .
Mathematics
1 answer:
Wewaii [24]3 years ago
3 0

Answer:

Dependent

x=3-3z

y=-5z-1

Step-by-step explanation:

We are given that system of equations

2x-3y-9z=9 (Equation I)

x+3z=3 ( Equation II)

-3x+y-4z=-10 (Equation III)

Equation III multiply by 3 and then add to equation I then we get

-7x-21z=-21

Divided by -7 then we get

x+3z=3

Now , obtained equation subtract from equation II then we get

0=0

Hence, equation II is a linear combination of equation I and equation III.

Therefore, system is dependent because system has infinite solutions.

x=3-3z

Substitute the value of x in equation I then we get

2(3-3z)-3y-9z=9

6-6z-3y-9z=9

3y=-15z+6-9=-15z-3

y=-5z-1

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