Consider the 3 by 3 system of equations: x-3y-5z=-5, 4x-2y+3z=13, 5x+3y+4z=22

Question

A.) show how to create a 2 by 2 system of equations by eliminating the variable “x” and then state your 2 by 2 system

b.) now solve the 2 by 2 system for “y” and “z”

c.) now state the final solution to the original 3 by 3 system as an ordered triple.

Answer 1

Multiply the first equation by - 4 and add it to the second equation.

-4x+12y+20z=20

4x - 2y + 3z=13

10y+23z=33

Multiply the first equation by - 5 and add it to the third equation.

-5x+15y+25z=25

5x + 3y + 4z=22

18y+29z=47

the two by two system

10y+23z=33

18y+29z=47

Solve this system for y and z.