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Question 553434: solve the system of equations using the substitution method
x+z=8
y-z=5
x-y=9
Found 3 solutions by Theo, ikleyn, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your 3 equations are:
x+z=8 (first equation)
y-z=5 (second equation)
x-y=9 (third equation)
from the first equation you get x = 8-z
from the second equation you get y = z+5
substitute for x and y in the third equation to get:
8-z - (z+5) = 9
simplify to get:
8-z-z-5 = 9
combine like terms to get:
3-2z = 9
subtract 3 from both sides of the equation to get:
-2z = 6
divide both sides of the equation by -2 to get:
z = -3
substitute for z in first equation to get:
x = 11
substitute for z in the second equation to get:
y = 2
your solution set is:
x = 11
y = 2
z = -3
substitute in all 3 original equations to get:
x+z=8 becomes 11-3 = 8 which becomes 8 = 8
y-z=5 becomes 2+3 = 5 which becomes 5 = 5
x-y=9 becomes 11-2 = 9 which becomes 9 = 9
solutions are confirmed as good.
Answer by ikleyn(52900)  (Show Source):
You can put this solution on YOUR website! .
solve the system of equations using the substitution method
x+z=8
y-z=5
x-y=9
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Yes, the substitution method is robust and works perfectly, as tutor @Theo showed in his post.
But I will show you even more effective method.
Add all the three equations. Then, after combining like terms, you will get
2x = 8 + 5 + 9 = 22.
Hence, x = 22/2 = 11.
Having it, you find from the first equation
z = 8 - x = 8 - 11 = -3,
and from the second equation
y = 5 + z = 5 + (-3) = 2.
ANSWER. x = 11, y = 2, z = -3.
Solved.
It is a kind of the Elimination method.
Resume: the Substitution method is good, but sometimes other methods
are more effective than the Substitution method.
Answer by MathTherapy(10557)  (Show Source):
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