Answer:
- (x, y, z) = (-5, -1, 0)
- (x, y, z) = (-8, -7, 5)
Step-by-step explanation:
1. A graphing calculator or equation-solving web site can tell you the solution is (-5, -1, 0).
As is sometimes the case with multiple-choice questions, you can choose the "consensus answer".
For x, -5 appears in 3 of 4 answer choices.
For y, -1 appears in 3 of 4 answer choices.
For z, 0 appears in 3 of 4 answer choices.
Thus, the "consensus" is that the answer is (-5, -1, 0). Choosing this one to check can shorten the work of checking the answer choices.
- -5 +5(-1) +4(0) = -10 . . . first equation can use this answer
- 2(-5) -(-1) +5(0) = -9 . . . second equation can use this answer
- 2(-5) -10(-1) -5(0) = 0 . . . third equation can use this answer
So, by "guess and check" we have determined the solution to be (-5, -1, 0).
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2. First of all, you can substitute the given value of z into the other two equations. Then you have ...
- 2x -y +5 = -4
- -2x +3y -5 = -10
The first of these equations can be solved for y:
y = 2x +9
and this can be substituted for y in the second of these equations:
-2x +3(2x +9) -5 = -10
4x +22 = -10
4x = -32
x = -8
and ...
y = 2(-8) +9 = -7
So this solution, too, is the "consensus solution," ...
(x, y, z) = (-8, -7, 5)
