Using complete sentences, explain which method you would use to solve the following system of equations and why. In your answer, include the solution to one of the variables and how you found it using the method you chose.

2x + y + z = –7
x – 3y + 4z = –14
x – 2y – 3z = –11

Question

Using complete sentences, explain which method you would use to solve the following system of equations and why. In your answer, include the solution to one of the variables and how you found it using the method you chose.

2x + y + z = –7
x – 3y + 4z = –14
x – 2y – 3z = –11

chaise · Answer

1. Multiply the first equation by four and then take away equation one from equation two to eliminate the z variable.
You will get a equation with two variables. 

2. Leaving the second equation how it was earlier, multiply it by 4, multiply the third equation by 4. Eliminate the z variable by adding the two equations together. Combined with step one you now have two equations you can solve simultaneously.

3. Follow the standard simultaneous solution procedure, making sure you substitute your values back into the original equation for z and not just y and x.

anonymous · Answer

subtract3rd equation from second. this eliminates x and gives you an equation in y and z.
multiply 2nd equation by 2 and subtract the result from first equation to get another equation in y and z.
solve these two equations to obtain values for y and z.
finally substitute theses values of y and z in to the first original equation to find z.

chaise · Answer

2. Leaving the second equation how it was earlier, multiply it by 3, multiply the third equation by 4. Eliminate the z variable by adding the two equations together. Combined with step one you now have two equations you can solve simultaneously.*

anonymous · Answer

2x+y+z=-7 (eq1)
x-3y+4z=-14 (eq2)
x-2y-3z=-11 (eq.3)

elim x in eq 2 by using eq 1

   2x+y+z=-7
-2(x-3y+4z=-14)= -2x+6y-8z=28 so:

        2x+y+z=-7
   + -2x+6y-8z=28
-------------------
             7y-7z=21

try to continue..=)

anonymous · Answer

2x + y + z = –7.................a
x – 3y + 4z = –14
multiply above by 2
2x - 6y + 8z = -28.............b

subtract  a - b:
7y -7z = 21..........................c

x – 3y + 4z = –14
x – 2y – 3z = –11
subtract 
-y + 7z = -3..........................d

add c + d
6y = 18
y = 3

7*3 - 7z = 21
z = 0
find x by plugging values of z and y into one of original equations