SOLUTION: Solve the system, if possible
x - 4y + z= 9
3y -2z= -7
-x +z= 0
Worked on these problems for over 3 hours and got nowhere. plase help
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Question 192037This question is from textbook College Algebra with Modeling and Visualization
: Solve the system, if possible
x - 4y + z= 9
3y -2z= -7
-x +z= 0
Worked on these problems for over 3 hours and got nowhere. plase help
This question is from textbook College Algebra with Modeling and Visualization
Found 2 solutions by stanbon, ankor@dixie-net.com:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
x - 4y + z= 9
0 + 3y -2z= -7
-x + 0 +z= 0
--------------------------
Add the 1st row to the 3rd to get:
---
x - 4y + z = 9
0 + 3y -2z =-7
0 + -4y +2z= 9
-------------------
Add the 2nd row to the 3rd row to get:
x - 4y + z = 9
0 + 3y -2z =-7
0 + -y + 0= 2
--------------------
The 3rd row tells you y = -2
---
Substitute into the 2nd row to solve for "z":
3(-2) - 2z = -7
-6 -2z = -7
-2z = -1
z = 1/2
--------------------------------
Substitute into the 1st row to solve for "x":
x - 4y + z = 9
x -4(-2) + (1/2) = 9
x + 8 1/2 = 9
x = 1/2
==================
Cheers,
Stan H.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Solve the system, if possible
x - 4y + z= 9
3y -2z= -7
-x +z= 0
;
let's rewrite it and add:
x - 4y + z = 9
0x +3y -2z = -7
-x +0y + z = 0
----------------Addition eliminates x and z
-y = 2
y = -2
:
Find z using the 2nd original equation
3(-2) - 2z = -7
-6 - 2z = -7
-2z = -7 + 6
-2z = -1
z =
z = +.5
;
Find x using the last original equation:
-x + .5 = 0
-x = -.5
x = + .5
:
Solutions: x=.5; y=-2; z=.5
:
Check solution in 1st original equation x - 4y + z = 9
.5 - 4(-2) + .5 = 9
.5 + 8 + .5 = 9
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