SOLUTION: Please help me solve this system of equations: Directions: Solve using elimination and using the matrix method x+y+z=6 2x-3y+5z=-11 x+3y-4z=19 Work I have done so far:

Question 660956: Please help me solve this system of equations:
Directions: Solve using elimination and using the matrix method
x+y+z=6
2x-3y+5z=-11
x+3y-4z=19
Work I have done so far:
x+y+z=6
-x-3y+4z=-19 This equals -2y+5z=-13 equation #1
-2x-6y+8z=-38
2x-3y+5z=-11 This equals -9y+13z=-49 equation #2
Multiply equation #1 by -9 and multiply equation #2 by 2
18y+45z=117
-18y-26z=-98 z= -19/71
At this point I got stuck because my teacher said that all answers would be nice even numbers. When I solved the equations using the matrix method (I know how to do this part) I got (3,4,-1) which I checked and is the correct answer.

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

Please help me solve this system of equations:
Directions: Solve using elimination and using the matrix method
x+y+z=6
2x-3y+5z=-11
x+3y-4z=19
Work I have done so far:
x+y+z=6
-x-3y+4z=-19 This equals -2y+5z=-13 equation #1
-2x-6y+8z=-38
2x-3y+5z=-11 This equals -9y+13z=-49 equation #2
Multiply equation #1 by -9 and multiply equation #2 by 2
18y+45z=117
-18y-26z=-98 z= -19/71
At this point I got stuck because my teacher said that all answers would be nice even numbers. When I solved the equations using the matrix method (I know how to do this part) I got (3,4,-1) which I checked and is the correct answer.

It would seem as though you multiplied - 9y + 13z = - 49 by 2, which results in: - 18y + 26z = - 98, NOT - 18y - 26z = - 98. This is where you went wrong. Look into this and you should be fine. My elimination-solution is below.

- 2x � 2y � 2z = - 12 ------- Multiplying eq (i) by � 2 ------ eq (iv)

� 5y + 3z = - 23 ------- Adding eqs (iv) and (ii) ----- eq (v)
- 2y + 5z = - 13 ------- Subtract eq (iii) from eq (i) ----- eq (vi)

10y � 6z = 46 ------- Multiplying eq (v) by � 2 ------ eq (vii)
- 10y + 25z = - 65 ------- Multiplying eq (vi) by 5 ------ eq (viii)
19z = - 19 -------- Adding eqs (viii) & (vii)
z = , or

� 5y + 3(- 1) = - 23 ------- Substituting � 1 for z in eq (v)
- 5y � 3 = - 23
� 5y = - 23 + 3
� 5y = - 20
y = , or

x + 4 - 1 = 6 ----- Substituting 4 for y and � 1 for z in eq (i)
x + 3 = 6
x = 6 - 3, or

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