Solve the following system of equations Enter your answers a

Solve the following system of equations. (Enter your answers as a comma-separated list. If there are infinitely many solutions, enter a parametric solution using t and/or s. If there is no solution, enter NONE.)

3y + 2z = 4

2x y 3z = 2

2x + 2y z = 6

Solution

3y + 2z = 4
2x y 3z = 2
2x + 2y z = 6

Subtracting the seocnd and third equation :
2x + 2y z = 6
2x y 3z = 2

We get :
3y + 2z = 4

This is just the first equation

When we solved the second and third,
we got the first

So this has infinitely many solutions

Using 3y + 2z = 4, we get :

Lets put z = s...
So, 3y + 2s = 4
y = (4 - 2s)/3

And using the second or third equation, we can get x now :

2x + 2(4-2s)/3 - s = 6

2x + (8 - 4s)/3 - s = 6

6x + 8 - 4s - 3s = 18

6x = 7s + 10

x = (7s + 10)/6

So, solution is :

x = (7s + 10)/6

y = (4 - 2s)/3

z = s