Solve the following system of equations using the
Tons using the Gaussian Method of elimination.
x - 2y + z = 6
3x + y -z = 7
4x - y + 2z = 15

Use the guide line in the photo to follow the steps how todo it

x = 3, y = - 1, z = 1

Step-by-step explanation:

listing the coefficients

1   - 2   1   6 ← R1

3    1    - 1  7 ← R2

4   - 1     2   15 ← R3

We require the first entry in R2 to be 0 while retaining R1 and the first 2 entries of R3 to be 0, thus

R2 - 3R1 and R3 - 4R1

1   - 2   1    6 ← R1

0    7   - 4  - 11 ← R2  

0    7    - 2  - 9 ← R3

Now R3 - R2

1    - 2    1     6 ← R1

0     7   - 4   - 11 ← R2

0    0      2    2 ← R3

From R3

2z = 2 ⇒ z = 1

Substitute z = 1 into R2

7y - 4(1) = - 11

7y - 4 = - 11 ( add 4 to both sides )

7y = - 7 ⇒ y = - 1

Substitute y = - 1, x = 1 into R1

x - 2(- 1) + 1 = 6

x + 2 + 1 = 6

x + 3 = 6 ( subtract 3 from both sides )

x = 3

Solution is (3, - 1, 1 )

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.

1) is right

step-by-step explanation: