4. what is the solution to the system of equations?
3x + 2y + z = 9
-3x-y+ 3z= -7
| 2x + z= 9
o (4, -2, -1)
© (4, 2, 1)
o (4, -2, 1)
• (-4, -2, 1)

Step-by-step explanation:

2x + z = 9z = -2x + 9

so we r gonna sub in -2x + 9 for z in our other 2 equations

3x + 2y + z = 9                                     -3x - y + 3z = -7

3x + 2y + (-2x + 9) = 9                         -3x - y + 3(-2x + 9) = -7

3x + 2y - 2x + 9 = 9                             -3x - y - 6x + 27 = -7

x + 2y = 9 - 9                                        - 9x - y = -7 - 27

x + 2y = 0                                              -9x - y = - 34

now we take our results and eliminate a variable

x + 2y = 0

-9x - y = -34multiply by 2

x + 2y = 0

-18x - 2y = - 68 (result of multiplying by 2)

add

-17x = -68

x = -68/-17

x = 4

now we sub 4 in for x in either of our resulting equations

x + 2y = 0

4 + 2y = 0

2y = 0 - 4

2y = -4

y = -4/2

y = -2

now that we know x and y, sub these values in to any of the original equations to find z

z = -2x + 9

z = -2(4) + 9

z = -8 + 9

z = 1

check it...

3x + 2y + z = 9

3(4) + 2(-2) + 1 = 9

12 - 4 + 1 = 9

8 + 1 = 9

9 = 9 (correct)...and it checks out

solution is : (4,-2,1) <