What is the solution to the system of equations?

We can solve this system of equations in the few ways:

1) With Gaussian algorithm

2) Matrix method

3) Kramer's rule with determinants

We will use Gaussian algorithm because it is easiest and I don't have

necessary graphic tools to show the procedure for the other methods.

3x+2y+z= 7

5x+5y+4z= 3

3x+2y+3z= 1  

We will multiply first equation with number (-1) and get

-3x-2y-z= -7 , then we add this equation to the third equation

consequence- variable x and y are eliminated and we get

-z+3z= -7+1 => 2z=-6 => z=-6/2 => z= -3

We replace variable z in the first two equations and get

3x+2y-3=7 => 3x+2y= 10

5x+5y+4*(-3)= 3 => 5x+5y-12=3 => 5x+5y= 15 we divide this equation with number 5 and get  x+y= 3  Finally we get next new system

3x+2y=10

x+y=3  we multiply second equation with number (-2) and get

-2x-2y= -6 then we add this equation to the first and get

consequence - we eliminated variable y

3x-2x=10-6 => x=4  we replace variable x in the second equation before multiplying and get  4+y=3 => y=3-4= -1 => y= -1

The solution of the system is (x,y,z) = ( 4, -1, -3 )

Good luck!!!

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step-by-step explanation: