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Question 447248: Find the ordered triple of these equations.
x - y + z = -8
y = 4
x + y - z = 6
Answer by Leaf W.(135)   (Show Source):
You can put this solution on YOUR website! ***First, since it tells you the value for y, you can just plug that in as the value for y in the other two equations:
x - y + z = -8 ==> x - 4 + z = -8 ==> (add 4 to both sides) x + z = -4
x + y - z = 6 ==> x + 4 - z = 6 ==> (subtract 4 from both sides) x - z = 2
Then, solve as a system of equations in two variables:
***"Add" the two equations:
x + z = -4
+(x - z = 2)
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2x + 0z = -2
Simplify: 2x = -2
Divide both sides by 2: x = -1
Therefore, x is -1.
***Plug this value for x into either of the two equations (x + z = -4 OR x - z = 2): -1 + z = -4
Solve for z:
Add 1 to both sides: z = -3
Therefore, z is -3.
==> If x = -1, y = 4, and z = -3, then (following the coordinate format (x,y,z)), your answer is (-1,4,-3).
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