Question

100 Points

Answer 1

Answer:

1) Consistent Independent

2) Coincident

3) Inconsistent

Step-by-step explanation:

Answer 2

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

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

$\left\{\begin{array}{ccc}3x+y=4\\3x+y=4\end{array}\right\Rightarrow\boxed{\text{coincident}}$