SOLUTION: Solve the system for each variable: y+z=6 x+5y-4Z=4 x-3y+5z=7

Question 54149: Solve the system for each variable:
y+z=6
x+5y-4Z=4
x-3y+5z=7
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
y+z=6
x+5y-4Z=4
x-3y+5z=7
:
Take the last two equations and eliminate x:
x + 5y - 4z = 4
x - 3y + 5z = 7
----------------subtract
0x +8y - 9z = -3
:
Using the 1st equation for substitution for y in 8y - 9z = -3:
y + z = 6
y = (6-z)
:
8(6-z) - 9z = -3
48 - 8z - 9z = - 3
-17z = -3 -48
-17z = -51
z = -51/-17
z = +3
:
:
Find y using the 1st equation, substituting 3 for z
y + z = 6
y + 3 = 6
y = 6 - 3
y = + 3 also
:
Find x using the 2nd equation, substituting 3 for y and z
x + 5y - 4z = 4
x +5(3) - 4(3) = 4
x + 15 - 12 = 4
x + 3 = 4
x = 4 - 3
x = +1
:
Check all three solutions in the 3rd equation:
x - 3y + 5z = 7
1 - 3(3) + 5(3) =
1 - 9 + 15 = 7; seems to be correct
:
Make sense to you??

RELATED QUESTIONS
Write the augmented matrix for each system of equations x + 3y = 5 y - 4z = 8 -2x = 5z (answered by venugopalramana)

2x + 3z = 4 3y + 2z = 5 3x + 4y = −16 (x, y, z) = 2x +... (answered by Alan3354)

Systems of Equations 1. Solve the following problems for X and Y i these two system... (answered by Alan3354)

1.Solve the following problems fo X and Y in these two system equation, and for X and Y,... (answered by solver91311)

How do I solve the system of equations? x+2y-6=z 3y-2z=7... (answered by gonzo)

Solve the system using any algebraic method. x+2y-6z=23 x+3y+z=4... (answered by ankor@dixie-net.com)

5x + 5y - 4z = 13 5x + 3y + z = - 3 3x - 2y - z = - 10 x=___ y=___ z=___ (answered by Alan3354)

Which answer correctly shows the first step that can be used to correctly solve the... (answered by Edwin McCravy)

Solve the system by elimination. -x-5y-5z=2 4x-5y+4z=19... (answered by Fombitz)