liyuhh16
Answered

What is the solution to this system of equations?
x + 3y - z = 6
4x - 2y + 2z= -10
6x + z= -12

(an explanation would be great because i barely understand how to do this)

Answer :

muhammadolim

Answer:

[tex]x=-3, y=5, z=6[/tex]

Step-by-step explanation:

1. Divide by 2 both sides in the second equation:

  • [tex]4x - 2y + 2z= -10[/tex]
  • [tex]2x - y + z= -5[/tex]

2. From the third equation find z in terms of x:

  • [tex]6x + z= -12[/tex]
  • [tex]z= -6x-12[/tex]

3. Add up the first and new second equations and find y in terms of x:

  • [tex](x+2x)+(3y-y)+(-z+z)=6+(-5)[/tex]
  • [tex]3x+2y=1[/tex]
  • [tex]2y=1-3x[/tex]
  • [tex]y=0.5-1.5x[/tex]

4. Put new alternatives instead of y and z in the first equation:

  • [tex]x+3(0.5-1.5x)-(-6x-12)=6[/tex]
  • [tex]x+1.5-4.5x+6x+12=6[/tex]
  • [tex]2.5x=-7.5[/tex]
  • [tex]x=-3[/tex]

5. Now we can easily find other two unknowns by using their equations by means of x:

  • [tex]y=0.5-1.5\times(-3)[/tex]
  • [tex]y=0.5+4.5[/tex]
  • [tex]y=5[/tex]
  • [tex]z=-6\times(-3)-12[/tex]
  • [tex]z=18-12[/tex]
  • [tex]z=6[/tex]
meredith48034

Answer:

Step-by-step explanation:

2x + 6y - 2z = 12

12x - 6y + 6z = -30

14x + 4z = -18

6x + z = -12

14x + 4z = -18

-24x - 4z = 48

-10x = 30

x = -3

6(-3) + z = -12

-18 + z = -12

z = 6

-3 + 3y - 6 = 6

-9 + 3y = 6

3y = 15

y = 5

x = -3, y = 5, z = 6

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