Answer:
<h2>infinitely many solutions</h2>
Step-by-step explanation:
5x - 6 = 3x - 6 + 2x <em>combine like terms</em>
5x - 6 = (3x + 2x) - 6
5x - 6 = 5x - 6 <em>subtract 5x from both sides</em>
-6 = -6 TRUE
Therefore the equation has infinitely many solutions.
<h3>
Answers:</h3>
Variation Constant: k = 7/6
y = 245/6 when x = 7 and z = 5
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Explanation:
"y varies jointly as x and z" means that y = kxz
We have (x,y,z) = (4,14,3) as one triple, so,
y = kxz
14 = k*4*3
14 = 12k
12k = 14
k = 14/12
k = 7/6 is the variation constant
The equation goes from y = kxz to y = (7/6)xz
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Plug in x = 7 and z = 5 to find y
y = (7/6)xz
y = (7/6)*7*5
y = (7/6)*(7/1)*(5/1)
y = (7*7*5)/(6*1*1)
y = 245/6
1 is perpendicular bc it's the opposite reciprocal so Basically it's the original fraction upside down. 2 is parallel bc both fractions have the same slope but one is negative
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Add sides 1


Subtract sides 4z



Divide sides by 6


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Subtract sides y


Divide sides by 2


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Thus the correct answer is :

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So, I'm going to break it down to help you understand it a bit more.
If it starts at (0,-2) and crosses through (1,0) that means it moved to the right once and up twice. Which means, that the slope will be 2. If it were one it would be to the right 1 up one, if it were 4 it would be to the right 1 up 4, and finally if it were 1/2 it would be to the right 2 up 1.
So, your answer is C. or 2.