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

Answer 1

the method I have used is Elimination, Why? it is easy and fast
1) 2x + y + z = –7
2) x – 3y + 4z = –14
3) x – 2y – 3z = –11

elimination of x
2) - 3) -y + 7z = - 3
1) - 2.3) 5y +7z = 15
now we solve the simple system

-y + 7z = - 3 a)
5y +7z = 15 b)

elimination of y
5. a) + b) implies 42 z=12 and z= 2/7
-y +7 . 2/7= -3 implies y = 5
y=5, z =2/7, so 2x + 5 + 2/7 = –7 implies x= - 43/7
final solution
x= - 43/7, y=5 and z =2/7

proof
2.(- 43/7) + 5 + 2/7 = -7, (true)