SOLUTION: Solve the following system of equations for the unknown variables. 2x + y = 17 y + z = 6 x – z = 7

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve the following system of equations for the unknown variables. 2x + y = 17 y + z = 6 x – z = 7       Log On


   

Question 143784: Solve the following system of equations for the unknown variables.
2x + y = 17
y + z = 6
x – z = 7

Found 2 solutions by ankor@dixie-net.com, scott8148:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
2x + y + 0 = 17
0x + y + z = 6
x + 0 – z = 7
-----------------adding eliminates z
3x + 2y = 30
:
multiply the 1st equation by 2 and subtract the above equation
4x + 2y = 34
3x + 2y = 30
-----------------subtracting eliminates y
x = 4
:
Use x - z = 7 to find z
4 - z = 7
-z = 7 - 4
-z = 3
z = -3
:
You should be able to find y

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
subtracting z from 2nd equation __ y=6-z

adding z to 3rd equation __ x=7+z

substituting into 1st equation __ 2(7+z)+(6-z)=17 __ distributing __ 14+2z+6-z=17

20+z=17 __ subtracting 20 __ z=-3

substituting __ y+(-3)=6 __ adding 3 __ y=9

substituting __ x-(-3)=7 __ adding -3 __ x=4