Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Discover a wealth of knowledge from professionals across various disciplines on our user-friendly Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

The solution to the system is x= , y= , z=

The Solution To The System Is X Y Z class=

Sagot :

The solution to the given system of equations is:

[tex](x, y, z) = \left(-\frac{87 + 111z}{11}, -\frac{15z + 18}{11}, z\right)[/tex]

There are infinite solutions for the system in the above format, you can choose the value of z and from this value find values for x and y.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

Applying the multiplication of the matrices, the equations are given as follows:

  • 2x + 6y + 12z = -6.
  • x + 3y + 6z = -3.
  • 3x - 2y + 3z = 8.

From the first equation, we have that:

2x = -6 - 6y - 12z

x = -3 - 3y - 6z

Replacing in the second equation, we have that:

-3 - 3y - 6z + 3y + 6z = -3

0z = 0

z = any value.

Hence we write the solutions as function of z.

Replacing in the third equation, we have that:

3x - 2y + 3z = 8.

3(-3 -3y - 6z) - 2y + 3z = 8

-9 - 9y - 18z - 2y + 3z = 9

-11y - 15z = 18

11y = -15z - 18.

[tex]y = \frac{-15z - 18}{11}[/tex]

The solution for x is:

x = -3 - 3y - 6z

[tex]x = -3 - \frac{45z + 54}{11} - 6z[/tex]

[tex]x = \frac{-33 - 45z - 54 - 66z}{11}[/tex]

[tex]x = -\frac{87 + 111z}{11}[/tex]

The solution for the system is:

[tex](x, y, z) = \left(-\frac{87 + 111z}{11}, -\frac{15z + 18}{11}, z\right)[/tex]

More can be learned about a system of equations at https://brainly.com/question/24342899

#SPJ1

Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.