Answer:
Step-by-step explanation:
2x + z = 9.....z = -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 = -34.....multiply 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) <====
