SOLUTION: 2x + y = 5 −x − 2y + 8z = 8 −y + 4z = 6 This is my first question! find, x,y,z and make sure that they are all true! 3x + 4y + z = 15 x − 2y + z = −15 2x + y + z

Algebra ->  Linear-equations -> SOLUTION: 2x + y = 5 −x − 2y + 8z = 8 −y + 4z = 6 This is my first question! find, x,y,z and make sure that they are all true! 3x + 4y + z = 15 x − 2y + z = −15 2x + y + z      Log On


   

Question 1151845: 2x + y = 5
−x − 2y + 8z = 8
−y + 4z = 6
This is my first question! find, x,y,z and make sure that they are all true!
3x + 4y + z = 15
x − 2y + z = −15
2x + y + z = 5
This is my second question! find, x,y,z and make sure that they are all true!
thank you to whoever answers this correctly! thanks
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Make an effort.
email for assistance if needed.
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You don't learn anything by just getting the answer.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

I'll get you started on each problem.

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Problem 1 
2x+y = 5 ............ equation (1)
-x - 2y + 8z = 8 .... equation (2)
-y + 4z = 6 ......... equation (3)


Note how there's a 'y' term in the first equation that has a coefficient of 1. This allows us to easily solve for y without involving fractions.
2x+y = 5
2x+y-2x = 5-2x
y = -2x+5

This can be plugged into the other equations to get rid one of the variables

Let's plug it into equation (2)
-x - 2y + 8z = 8
-x - 2( y ) + 8z = 8
-x - 2( -2x+5 ) + 8z = 8 .... replace y with -2x+5, y is eliminated temporarily
-x + 4x - 10 + 8z = 8
3x - 10 + 8z = 8
3x - 10 + 8z + 10 = 8 + 10 ... add 10 to both sides
3x + 8z = 18 .... Call this equation (4)


Plug y = -2x+5 into equation (3) now
-y + 4z = 6
-( y ) + 4z = 6
-( -2x+5 ) + 4z = 6
2x - 5 + 4z = 6
2x - 5 + 4z+5 = 6+5 ... add 5 to both sides
2x + 4z = 11 .... Call this equation (5)


The system of equations we were given reduces to this
3x + 8z = 18 .... Equation (4)
2x + 4z = 11 .... Equation (5)

I'll let you take over from here.

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Problem 2 

3x + 4y + z = 15 .... equation (1)
x - 2y + z = -15 .... equation (2)
2x + y + z = 5 ...... equation (3)


Solve equation (1) for z
3x + 4y + z = 15
3x + 4y + z-3x = 15-3x .... subtract 3x from both sides
4y+z = 15-3x
4y+z-4y = 15-3x-4y .... subtract 4y from both sides
z = -3x-4y+15

Move onto equation (2) and plug in z = -3x-4y+15
x - 2y + z = -15
x - 2y + ( z ) = -15
x - 2y + ( -3x-4y+15 ) = -15 ... replace z with -3x-4y+15
x - 2y - 3x-4y+15 = -15
-2x - 6y + 15 = -15
-2x - 6y + 15-15 = -15-15
-2x - 6y = -30 .... call this equation (4)

Do the same for equation (3)
2x + y + z = 5
2x + y + (z) = 5
2x + y + (-3x-4y+15) = 5 ... replace z with -3x-4y+15
2x + y - 3x-4y+15 = 5
-x -3y + 15 = 5
-x -3y + 15-15 = 5-15
-x -3y = -10 .... call this equation (5)


Equations (4) and (5) form a simpler system
-2x - 6y = -30
-x - 3y = -10

I'll let you solve this system.
Once you know x and y, use those values to find z.