Please Help Algebra

Question

Solve the system of equations.
5x + 2y + z = -11
2x – 3y – z = 17
7x + y + 2z = -4


1) {(0, -6, 1)}

2) {(-3, 0, 4)}

3) {(3, 0, -4)}

4) {(0, 6, -1)}

 

Please explain. Failing my Algebra I apologize if i post a lot of questions i just need to make a good grade on this assignment.

Answer 1

Let's use Gaussian elimination.

 

System:

 

(i): 5x + 2y + z = -11
(ii): 2x – 3y – z = 17
(iii): 7x + y + 2z = -4

 

 

Adding equations (i) and (ii) together gives:

 

(i)+(ii): 7x - y = 6

 

Adding adding twice equation (ii) to equation (iii) gives:

 

2(ii) + (iii): 11x - 5y = 30

 

New system:

 

(iv) 7x - y = 6

(v) 11x - 5y = 30

 

Multiply (iv) by 5 and then subtract (v).

 

5(iv): 35x - 5y = 30

 

5(iv) - (v): 24x = 0

 

x = 0

 

Now back-substitute:

 

7x - y = 6

 

0 - y = 6

 

y = -6

and

 

2x – 3y – z = 17

 

0 + 18 - z = 17

 

1 - z = 0

 

z = 1

 

Let's plug in x = 0, y = -6, z = 1, to verify that this is indeed the solution:

 

5x + 2y + z = 5(0) + 2(-6) + 1 = 0 - 12 + 1 = -11

 

2x – 3y – z = 2(0) - 3(-6) - 1 = 0 + 18 - 1 = 17

 

7x + y + 2z = 7(0) + (-6) +2(1) = 0 - 6 + 2 = -4

Answer 2

The answers provided are coordinates in a 3-dimensional system.  All you have to do is substitute the numbers into each equation to check and see if the equations are valid.  Once you find a coordinate that is valid in all 3 equations, you have found your solution to the system of equations.