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Solve the following system of equations for the unknown variables.

3x + 3y = 3

-3x – 2z = -11

y + z = -1

 Dec 23, 2018
 #1
avatar+4296 
+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 \((x,y,z)=(3,-2,1).\)

.
 Dec 23, 2018
edited by tertre  Dec 24, 2018
 #4
avatar+701 
+1

The correct answers are x = 3, y = -2, and z = 1.

 

- PM

PartialMathematician  Dec 24, 2018
 #5
avatar+701 
+1

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
avatar
+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 =                                           sub this into (2) above
-3x - 2(1) = - 11
-3x = - 9
x =-9 / -3
x = 3 ,     y = -2,     z = 1

 Dec 23, 2018
edited by Guest  Dec 24, 2018
 #3
avatar+701 
+1

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

PartialMathematician  Dec 24, 2018

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