ellistrina

In this case the two equations describe lines that intersect at one particular point. Clearly this point is on both lines, and therefore its coordinates (x, y) will satisfy the equation of either line. Thus the pair (x, y) is the one and only solution to the system of equations.

grujan50

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!!!