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Solve the following system of equations for the unknown variables.

3x + 3y = 3

-3x – 2z = -11

y + z = -1

Guest Dec 23, 2018

#1**+1 **

Add the first two equations: 3y-2z=-8

y+z=-1

Now, multiply the second equation by 2, so 2y+2z=-2. Then, subtract the first equation from the second: y=-8+2, y=-6.

-6+z=-1, z=-1+6=5

And, x equals 3x+3(-6)=3, 3x-18=3, 3x=21, x=7.

Thus, the answer is \((x,y,z)=(3,-2,1).\)

.tertre Dec 23, 2018

#5**0 **

I found your mistake. The sum of the first two equations is not 3y + 2z = -8.

3x + 3y = 3

+ -3x - 2z = -11

______________

3y - 2z = -8

Not 3y + 2z = -8.

PartialMathematician
Dec 24, 2018

#2**+1 **

3x + 3y = 3...........................(1)

-3x – 2z = -11.......................(2)

y + z = -1.............................(3)

From (3): z = -1 - y sub into (2)

3x + 3y =3.............................(1)

-3x -2 (-1 - y)= -11................(4)

-3x + 2 + 2y = - 11..............(5)

-3x + 2y = - 13......................(6) add this to (1) above

5y = - 10,

**y =** -10 / 5 =** -2 ** sub this into (3) above:

-2 + z = -1

**z =**-1 + 2 =**1 ** sub this into (2) above

-3x - 2(1) = - 11

-3x = - 9

x =-9 / -3

**x = 3 , y = -2, z = 1**

Guest Dec 23, 2018

edited by
Guest
Dec 24, 2018

#3**0 **

I checked both of your answers, and I found out that Guest's answers are correct.

PartialMathematician
Dec 24, 2018