solve by elimination: x + y + z = -3, 3y - z = 4, and 2x - y - 2z = -5.

Question

PLZ!!!! I need help!!! If you could show me an explanation  so I know how to do it in the future

2x - y - 2z = -5.

3y - z = 4,

x + y + z = -3

Write your answer as a point, an ordered triple: (x,y,z), without spaces

 

Answer 1

solve equations 1 and 3 by multiplying equation 3 by 2 and subtract the the result from equation 1

 

(2x-2x)+(2y-(-y))+(2z-(-2z))=-3(2)-(-5)

 

3y+4z=-1

 

solving the result equation with equation 2 by subtracting the equation from equation 2

 

5z=-5 --------> z=-1

 

substitution in equation 2

 

3y-(-1)=4 ------> 3y=4-1 ----->y=1

 

substitution in equation 3

 

x+1+(-1)=-3 -------> x=-3

 

the solution is x=-3, y=1, z=-1

 

Answer 2