How do you solve the system x +4y - 6z = 4, 4x - 3y + 2z = 26, x - 2y +2z = 8?

1 Answer
Nov 12, 2016

Answer:

Please see the explanation for step leading to the solution:

#x = 4, y = -6, z = -4#

Explanation:

Write the 3 equations as an augmented matrix:

#[ (1,4,-6,|,4), (4,-3,2,|,26), (1,-2,2,|,8) ]#

Multiply row 1 by -4 and add to row 2:

#[ (1,4,-6,|,4), (0,-19,26,|,10), (1,-2,2,|,8) ]#

Multiply row 1 by -1 and add to row 3:

#[ (1,4,-6,|,4), (0,-19,26,|,10), (0,-6,8,|,4) ]#

Multiply row 3 by -3 and add to row 2:

#[ (1,4,-6,|,4), (0,-1,2,|,-2), (0,-6,8,|,4) ]#

Multiply row 2 by -1:

#[ (1,4,-6,|,4), (0,1,-2,|,2), (0,-6,8,|,4) ]#

Multiply row 2 by 6 and add to row 3:

#[ (1,4,-6,|,4), (0,1,-2,|,2), (0,0,-4,|,16) ]#

Divide row 3 by -4:

#[ (1,4,-6,|,4), (0,1,-2,|,2), (0,0,1,|,-4) ]#

Multiply row 3 by 2 and add to row 2:

#[ (1,4,-6,|,4), (0,1,0,|,-6), (0,0,1,|,-4) ]#

Multiply row 3 by 6 and add to row 1:

#[ (1,4,0,|,-20), (0,1,0,|,-6), (0,0,1,|,-4) ]#

Multiply row 2 by -4 and add to row 1:

#[ (1,0,0,|,4), (0,1,0,|,-6), (0,0,1,|,-4) ]#

This means that #x = 4, y = -6, and z = -4#
You should check my answer by substution into the orignal equations.