SOLUTION: Please help me solve the system 2x-3y+4z= -14 4x+2y-3z= -17 6x-5y+7z= -37 find x,y,z

Question 1069131: Please help me solve the system
2x-3y+4z= -14
4x+2y-3z= -17
6x-5y+7z= -37
find x,y,z
Found 2 solutions by Alan3354, Boreal:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Similar problem:
=========================================================
Please help me solve the system
3x+2y-2z=14
2x-5y+3z=7
4x-3y+7z=5
================
I would eliminate x first.
Multiply the 1st eqn by 2 and the 2nd by 3, then subtract.
--> eqn in y & z
====================
Multiply the 2nd eqn by 2, subtract from the 3rd eqn.
--> another eqn in y & z
===============
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Set up the determinant matrix, which are the coefficients of the variables in a 3 x 3 matrix. Find the determinant, which is 8.
Put the column of constants in the first column of the above matrix, replacing those values with -14,-17, and -37. This will give the value for x, when divided by the 8 above.
Det (x)=-40/8=-5
Similarly, do y
Det (y)=-0
Det (z)=-8/8=-1
(-5, 0, -1) ANSWER
Check-10-4=-14
-20-(-3)=-17
-30-7=-37
RELATED QUESTIONS
Please help me solve the system 3x+2y-2z=14 2x-5y+3z=7 4x-3y+7z=5 Find, x, y,... (answered by Alan3354)
Solve. If the system's equations are dependent or it there is no solution, state this. (answered by Alan3354)
Solve. If the system's equations are dependent or it there is no solution, state this. (answered by solver91311)
Please help me solve this linear system with three variables. 2x-y+2z=-21 x+5y-z=25 (answered by Alan3354)
2x + 3z = 4 3y + 2z = 5 3x + 4y = −16 (x, y, z) = 2x +... (answered by Alan3354)
can someone PLEASE help me solve this system: { x+ y-4z=6 {2x-5y+3z=2 { x-6y+7z=-4... (answered by stanbon)
Extrememly confused, help please! Solve each system in three variables... (answered by stanbon)
please help me in finding x, y and z in the linear equation 2x-5y=2 -4x+3z=5... (answered by Alan3354)
Solve the system. 3x+2y-z=-8 2x-y+7z=33 2x+2y-3z=-17 x= y= z= *Attempted... (answered by Earlsdon)