Without Graphing, Is The System Independent, Dependent, Or Inconsistent? (Equation And Answer Choices Are In Comments!)

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Question:

13.) Write a Paragraph proof ( Thanks!!)

Given Line BC = Line EC and Line AC = DC Line
Prove Line BA= Line ED

Answer:

12x +3y = 12

y = -4x +5

 
We can convert the first equation to the same form as the second (y=mx+b, or slope-intercept).

 
12x +3y = 12

3y = -12x +12

y = -4x +4

 
Comparing the simplified first equation y = -4x +4 to the second equation y = -4x + 5, we see that both have the same slope (m = -4), but different y-intercepts (b = 4, b = 5). This means they are parallel lines, or an inconsistent system. There are no solutions.

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