Answer:
3/6
Step-by-step explanation:
Miles is going to spend fewer hours bicycling this week than he did last year.
X + 3y + 5z = 45
6x - 3y + 2z = - 10
------------------------add
7x + 7z = 35
6x - 3y + 2z = -10
-2x + 3y + 8z = 72
----------------------add
4x + 10z = 62
7x + 7z = 35....multiply by 4
4x + 10z = 62...multiply by -7
---------------------
28x + 28z = 140 (result of multiplying by 4)
-28x - 70z = - 434 (result of multiplying by -7)
--------------------add
- 42z = - 294
z = -294/-42
z = 7
4x + 10z = 62
4x + 10(7) = 62
4x + 70 = 62
4x = 62 - 70
4x = - 8
x = -8/4
x = -2
x + 3y + 5z = 45
-2 + 3y + 5(7) = 45
-2 + 3y + 35 = 45
3y + 33 = 45
3y = 45 - 33
3y = 12
y = 12/3
y = 4
solution is (-2,4,7) <==
It appears you have the system with augmented matrxi ...
Right away, you notice that the 4th row is 3 times the 2nd row, so the equations are dependent and will not have a unique solution.
My calculator tells me the reduced equations can be written
... x1 -14x3 -19x4 = -8
... x2 -12x3 -16x4 = -7
This says there are two dependent equations in the set, not just one.