Respuesta :

wegnerkolmp2741o

Answer:


Step-by-step explanation:

x+5y = -2

x+5y =4

these lines are parallel

they have the same slope but different y intercepts

inconsistent


y = 3x+4

-2x+y =4   y = 2x+4

different slopes  same y intercept

they intersect at one point

consistent and independent


3x+y =4     y = -3x+4

-6x-2y = -8    -2y =6x-8   y = -3x +4

same slope  same y intercept

they are the same line

consistent and dependent  (coincident)


gmany

[tex]\left\{\begin{array}{ccc}ax+by=c\\ax+by=c\end{array}\right\Rightarrow\text{coincident}\\\\\left\{\begin{array}{ccc}ax+by=c\\ax+by=d\\c\neq d\end{array}\right\Rightarrow\text{inconsistent}\\\\\left\{\begin{array}{ccc}ax+by=c\\dx+ey=c\\a\neq d\ or\ b\neq e\end{array}\right\Rightarrow\text{consistent independent}[/tex]

[tex]\left\{\begin{array}{ccc}x+5y=-2\\x+5y=4\end{array}\right\Rightarrow\boxed{\text{inconsistent}}\\--------------------------------\\\left\{\begin{array}{ccc}y=3x+4&\text{subtract 3x from both sides}\\-2x+y=4\end{array}\right\\\\\left\{\begin{array}{ccc}-3x+y=4\\-2x+y=4\end{array}\right\Rightarrow\boxed{\text{consistent independent}}\\-----------------------------\\\left\{\begin{array}{ccc}3x+y=4\\-6x-2y=-8&\text{divide both sides by (-2)}\end{array}\right\\[/tex]

[tex]\left\{\begin{array}{ccc}3x+y=4\\3x+y=4\end{array}\right\Rightarrow\boxed{\text{coincident}}[/tex]

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