1. Solve for x: -2x + y + 4z = -1 6x -3y -12z = 3 6x – 3y -z = 1 a. 2/3 b. Depen

Question

1. Solve for x:

-2x + y + 4z = -1

6x -3y -12z = 3

6x – 3y -z = 1

a. 2/3

b. Dependent

c. -2/3

d. Inconsistent

2. Solve for z:

2x + y -2z = 3

4x -y + 2z = 3

6x + 3y -z = 2

a. 5/7

b. Dependent

c. -7/5

d. Inconsistent

3. Solve for y:

-x -2y + z = 3

2x + 4y – 2z = 1

3x + 4y -7z = 0

a. Dependent

b. 12/5

c. Inconsistent

d. -5/12

4. Solve for z:

X + y + z = 5

2x – 3z = 7

3x – y +z = 1

5. Solve for z:

X + 2y – z = 1

2x + y + z = -1

X – y + 3z = 1

6. Solve for y:

3x + 3y – 2z = 10

X + 2y + z = 0

X -y -2z = 0

7. Solve for x:

2x – 9z = 9

2x + 3y = 9

X – y – 3z = 9

Explanation / Answer

Ans 1:

Step 1: Given equations in the question

-2x + y + 4z = -1

6x -3y -12z = 3

6x – 3y -z = 1

Step 2: We have to solve for x

Step 3: Consider first 2 equations

-2x + y + 4z = -1

6x -3y -12z = 3

if we divide the second equation by -3, we get,

6x/(-3) -3y/(-3) -12z(-3) = 3/(-3)

-2x + y +4z = -1, which is same as equation 1

Step 4: Since first 2 equations are same, we have 2 equations and 3 variables

Step 5: Hence, this is a dependent system of equations in which the same equation is written in different form

Step 6: The answer is B) Dependent

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