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what is the solution of the system of equations?
3x + 2y + z = 7
5x + 5y +4z = 3
3x +2y +3z = 1

You can start by subtracting different equations from each other.

3x + 2y + 3z = 1

subtract

3x + 2y + z = 7

2z = -6

divide by 2

z = -3

add the following two expressions together:

3x + 2y + z = 7

3x + 2y + 3z =1

6x + 4y + 4z = 8

subtract the following two expressions:

6x + 4y + 4z = 8

5x + 5y + 4z = 3

x - y = 5

^multiply the whole equation above by 3

3x - 3y = 15

subtract the following two expressions:

3x - 3y = 15

3x + 2y = 10

-5y = 5

divide each side by -5

y=-1

take the following expression from earlier:

x - y = 5

substitute y value into above equation

x - - 1 = 5

2 negatives make a positive

x + 1 = 5

subtract 1 from each side

x = 4

Therefore x = 4, y = -1, z = -3

I checked these with all 3 equations and they worked :)

(it's quite complicated, comment if you don't understand anything) :)

{3 + i, 3 - i, 3, -1}

step-by-step explanation: