narissa
  • narissa
Please Help!!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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narissa
  • narissa
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narissa
  • narissa
@Cardinal_Carlo
Nerdsarecool
  • Nerdsarecool
Where is d

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Nerdsarecool
  • Nerdsarecool
But first which number do we know is correct
narissa
  • narissa
@Nerdsarecool there is no D
anonymous
  • anonymous
If a system has an infinite number of solutions, it is dependently consistent. If it only has one solution, it is independently consistent. Otherwise, if it has no solution, then it is considered inconsistent. Let's take a look at the first system: \[x + 5y = -2\] \[x + 5y = 4\] If you rewrite these equations into point-slope form, you'll see that: \[m = -\frac{ 1 }{ 5 }\] However, each equation's y-intercept is different from the other. This indicates that these lines are parallel to each other but are a distance apart. Meaning, we won't find a single solution. We can therefore conclude that this system is inconsistent.
narissa
  • narissa
Oh okay would the 2nd one be B?
anonymous
  • anonymous
Well, coincidence refers to a system of equations where both equations are identical to each other. This is not the case for the second system. We see in the first equation that: \[m = 3\] And in the second equation that: \[m = 2\] Furthermore, they both have the same y-intercept: \[b = 4\] Meaning, that these two equations intersect at point (0, 4). Since there is only one solution for this system, we can conclude that this is a independently consistent system.
anonymous
  • anonymous
If you're looking for coincidence, observe the third system of equations. Notice how they're basically the same line. Of course, you'd have to put the second equation into point-slope form first in order to get a clearer view.
anonymous
  • anonymous
Try identifying the fourth system for fun. You're smart. I know you can do it @narissa.
narissa
  • narissa
okay ill try thank you
anonymous
  • anonymous
You're welcome
narissa
  • narissa
i think the lats one is C @Cardinal_Carlo
narissa
  • narissa
last*
anonymous
  • anonymous
You got close. Well, it was a good try. Notice in the first equation: \[m = -\frac{ 2 }{ 5 }\] But on the second equation: \[m = \frac{ 2 }{ 5 }\] Notice how the first equation has a positive slope while the second has a negative slope. This would mean that these two would cross only once. Therefore, we would call this one an independently consistent system.
anonymous
  • anonymous
To make it simple just follow these rules: Same line = coincident One intersection = consistent independent No intersections = inconsistent And to see how the lines interact with each other, try rewriting them in point-slope form. Or better yet, graph them.
narissa
  • narissa
thank u
anonymous
  • anonymous
You're welcome

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