6x-6y-4z=-10
-5x+4y-z=-12
2x+3y-2z=9
in Algebra 2 Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

6x-6y-4z=-10 -5x+4y-z=-12 2x+3y-2z=9

1)  6x - 6y - 4z = -10
2)  -5x + 4y - z = -12
3)  2x + 3y - 2z = 9

Multiply equation two by 4.
4 * (-5x + 4y - z) = -12 * 4
4)  -20x + 16y - 4z = -48

Subtract equation four from equation one.
      6x -    6y - 4z = -10
-(-20x + 16y - 4z = -48)
-----------------------------
   26x - 22y      = 38
5)  26x - 22y = 38

Multiply equation two by 2.
2 * (-5x + 4y - z) = -12 * 2
6)  -10x + 8y - 2z = -24

Subtract equation six from equation three.
      2x + 3y - 2z =    9
-(-10x + 8y - 2z = -24)
----------------------------
   12x - 5y      = 33
7)  12x - 5y = 33

Multiply equation five by 5.
5 * (26x - 22y) = 38 * 5
8)  130x - 110y = 190

Multiply equation seven by 22.
22 * (12x - 5y) = 33 * 22
9)  264x - 110y = 726

Subtract equation eight from equation nine.
  264x - 110y = 726)
-(130x - 110y = 190)
--------------------------
  134x        = 536
134x = 536
x = 4  <<<<<<<<<<<<<<<<<<<

Plug the value of x into equation seven.
12x - 5y = 33
12(4) - 5y = 33
48 - 5y = 33
-5y = -15
y = 3  <<<<<<<<<<<<<<<<<<<

Plug the values for x and y into equation two.
-5x + 4y - z = -12
-5(4) + 4(3) - z = -12
-20 + 12 - z = -12
-z = -12 + 20 - 12
-z = -4
z = 4  <<<<<<<<<<<<<<<<<<<

x = 4, y = 3, z = 4

Check the answers by plugging all three values
into the original equations.

One:
6x - 6y - 4z = -10
6(4) - 6(3) - 4(4) = -10
24 - 18 - 16 = -10
6 - 16 = -10
-10 = -10

Two:
-5x + 4y - z = -12
-5(4) + 4(3) - 4 = -12
-20 + 12 - 4 = -12
-8 - 4 = -12
-12 = -12

Three:
2x + 3y - 2z = 9
2(4) + 3(3) - 2(4) = 9
8 + 9 - 8 = 9
9 = 9

All values are correct.
by Level 11 User (78.4k points)

Related questions

1 answer
asked Jul 6, 2019 in Algebra 1 Answers by Sitaram Shendarkar | 248 views
1 answer
1 answer
1 answer
1 answer
asked Feb 27, 2019 in Algebra 2 Answers by Tallent Level 1 User (300 points) | 120 views
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
85,240 questions
90,465 answers
2,120 comments
78,575 users