Solve the system of equations.
2x + 2y + 3z = 5
6x + 3y + ôz = 6
3x + 4y + 4z = 9
a. (x = 0, y = 1, z = 0)
b. (x = 1, y = 0, z = 3)
c. (x = -2, y = 3, 2 = 2)
d. (x=-1, y = 2,2 = 1)

x=-1, y = 2, z = 1

Step-by-step explanation:

We are given with three equations and we are asked to find the solution to them.

2x + 2y + 3z = 5   (A)

6x + 3y + 6z = 6  (B)

3x + 4y + 4z = 9 (C)

Step 1 .

multiplying equation (A) by 3 and subtracting B from the result

6x + 6y + 9z = 15

6x + 3y + 6z = 6

-     -       -       = -

3y+3z=9

y+z=3

y=3-z   (C)

Step 2.

Substituting this value of y in equation B and C

6x + 3(3-z) + 6z = 6  

6x+9-3z+6z=6

6x+3z=-3

2x+z=-1 (D)

3x + 4(3-z) + 4z = 9

3x+12-4z+4z=9

3x=-3  

x=-1 (E)

Putting this value f x in (D)

2(-1)+z=-1

-2+z=-1

z=1

Now we put this value of z in equation (C)

y=3-z

y=3-1

y=2

Hence we have

x=-1, y=2 and z=1