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Question 1120943: x+y=5
y+z=7
z+x=6
by matrix method
Found 3 solutions by josgarithmetic, Alan3354, ikleyn:
Answer by josgarithmetic(39620)   (Show Source):
Answer by Alan3354(69443)  (Show Source):
Answer by ikleyn(52798)  (Show Source):
You can put this solution on YOUR website! .
This system of equations is VERY SPECIAL, and there is VERY SPECIAL trick to solve it.
x + y = 5 (1)
y + z = 7 (2)
z + x = 6 (3)
Add equations (1), (2) and (3) (both sides). You will get
2x + 2y + 2z = 5 + 7 + 6 = 18, or, equivalently,
x + y + z = 9. (4)
Now subtract equation (1) from equation (4). You will get z = 9-5 = 4.
Next subtract equation (2) from equation (4). You will get x = 9-7 = 2.
Finally, subtract equation (3) from equation (4). You will get y = 9-6 = 3.
Answer. The solution to the system is (x,y,z) = (2,3,4).
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For closely related/similar problems see the lesson
- The tricks to solve some word problems with three and more unknowns using mental math
in this site.
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