SOLUTION: What would be the easiest way to solve this problem ? The only known value is that z=9 x + Y + Z = 14 x

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Question 791782: What would be the easiest way to solve this problem ? The only known value is that z=9
x + Y + Z = 14
x - 2y = -4
Z = 9
Found 3 solutions by rothauserc, solver91311, DrBeeee:
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website!
What would be the easiest way to solve this problem ? The only known value is that z=9
*****from this statement and the given equations, one can assume without loss of generality that you meant z is equivalent to Z in this problem and Y is equivalent to y although in mathematics one must be consistent :-) *******
we are given
x + Y + Z = 14
x - 2y = -4
Z = 9
substitute for z in equation 1, this gives us two equations in two unknowns
x +y +9 = 14
x -2y = -4
subtract 9 from both sides of =
x +y = 5 and
x = 5 -y
substitute for x in the second equation
5 -y -2y = -4
subtract 5 from both sides of =
-3y = -9
y = 3
x +3 = 5
x = 2
check with second equation
2 -2*3 = -4
-4 = -4
answers check
x = 2, y = 3

Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!

You cannot find a unique solution to the problem as written. Y is NOT, under any circumstances the same thing as y. Hence you have four variables and only three equations, so the best you can do is find a relative solution.

On the other hand, if you really meant:

Then substitute 9 for in equation 1 to get:

Leaving you with the 2X2 system:

Multiply the 2nd equation by -1.

Add the two equations:

Substitute back into

The solution set is

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website!
Given
(1) z = 9
(2) x + y + z = 14
(3) x - 2y = -4
Substitute z of (1) into (2) and get
(4) x + y + 9 = 14 or
(5) x + y = 5
Now you have two equations, (5) and (3) to solve simultaneously for x and y. Use the following steps;
Subtract equation (3) from equation (5) as follows to get
(6) (x+y) - (x-2y) = 5 - (-4) or
(7) 3y = 9 or
(8) y = 3
Using (2) we get
(9) x = 14 - 9 - 3 or
(10) x = 2
Let's check the values with (1), (2) and (3).
Is (9 = 9)? Yes
Is (2 + 3 + 9 = 14)?
Is (14 = 14)? Yes
Is (2 - 2*3 = -4)?
Is (2 - 6 = -4)?
Is (-4 = -4)? Yes
Answer: {x,y,z} = {2,3,9). The easy way!
PS Don't mix upper case and lower case letters, y and Y, - they are different variables in mathematics and passwords.

SOLUTION: What would be the easiest way to solve this problem ? The only known value is that z=9 x + Y + Z = 14 x - 2y = -4 Z = 9