Question

PLZ HELP

What are the classifications of each system?

Drag the answer into the box to match each system.

Answer 1

`\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\\eq d\end{array}\right\Rightarrow\text{inconsistent}\\\\\left\{\begin{array}{ccc}ax+by=c\\dx+ey=c\\a\\eq d\ or\ b\\eq 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}}`

Answer 2

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)