Question

Use the elimination method to solve the following system of equations.

x + 3y – z = 2
x – 2y + 3z = 7
x + 2y – 5z = –21

(2, 3, 5)

(–2, 3, 5)

(2, –3, 5)

(2, 3, –5)

Answer 1

elimination is a methodical process. Often people start by writing just the coefficients (but keeping all the variables "lined up" in alphabetical order like ou have...

Answer 2

for example, start with
1 3 -1 2
1 -2 3 7
1 2 -5 -21

you start by zeroing out the numbers below 1 in the first column
to zero out the 1 in the 2nd row, multiply the first row by -1 and add that whole row to the 2nd row. You keep the first row as it is

Answer 3

1 3 -1 2 mutiply by -1 to get -1 -3 1 -2
add that to the 2nd row 1 -2 3 7
to get 0 -5 4 5
that is your new 2nd row

1 3 -1 2
0 -5 4 5
1 2 -5 -21

Answer 4

can you zero out the 1 in the 3rd row ? In this case all you do is add
-1 -3 1 -2 to the 3rd row

Answer 5

start with the first two equations and eliminate a variable...I eliminated x
x + 3y - z = 2 -->(-1)x + 3y - z = 2
x - 2y + 3z = 7
---------------
-x - 3y + z = - 2 (result of multiplying by -1)
x - 2y + 3z = 7
---------------add
0 - 5y + 4z = 5
-5y + 4z = 5

now take the last two equations and eliminate x
x - 2y + 3z = 7 -->(-1)x - 2y + 3z = 7
x + 2y - 5z = -21
----------------
-x + 2y - 3z = -7 (result of multiplying by -1)
x + 2y - 5z = - 21
-----------------add
0 + 4y - 8z = - 28
4y - 8z = - 28

now take the answers you got...the ones where the x's are eliminated
-5y + 4z = 5 -->(2)-5y + 4z = 5
4y - 8z = - 28
-----------------
-10y + 8z = 10 (result of multiplying by 2)
4y - 8z = - 28
----------------add
-6y = -18
y = - 18/-6
y = 3

now sub 3 in for y in either of the last two equations...
4y - 8z = - 28
4(3) - 8z = - 28
12 - 8z = - 28
-8z = - 28 - 12
-8z = - 40
z = -40/-8
z = 5

now sub 5 in for z and 3 in for y in any of the original equations...
x + 3y - z = 2
x + 3(3) - 5 = 2
x + 9 - 5 = 2
x + 4 = 2
x = 2 - 4
x = - 2

check...
x - 2y + 3z = 7
-2 - 2(3) + 3(5) = 7
-2 - 6 + 15 = 7
-8 + 15 = 7
7 = 7 (correct)

ANSWER : (-2, 3, 5)

Is there anything you do not understand ? If there is please ask. I will be happy to explain any of the work I have done. It is not hard, just time consuming.