Question

The shaded region in the graph below represents the solution set to which of the following systems of inequalities?

• A. $\{\begin{array}{c}y<-x+2\\ {(x-1)}^2+{(y-2)}^2<9\end{array}$
• B. $\{\begin{array}{c}y>-x+2\\ {(x-1)}^2+{(y-2)}^2<9\end{array}$
• C. $\{\begin{array}{c}y>-x+2\\ {(x-1)}^2+{(y-2)}^2>9\end{array}$
• D. $\{\begin{array}{c}y<-x+2\\ {(x-1)}^2+{(y-2)}^2>9\end{array}$
• E. $\{\begin{array}{c}(y-2)<3\\ (x-1)>3\end{array}$

Answer 1

Answer: (A)

$\{\begin{array}{c}y<-x+2\\ {(x-1)}^2+{(y-2)}^2<9\end{array}$

$(x-1{)}^2+(y-2{)}^2=9$

$y+x=2$

Substituting (0,0) in both equation

$(0-1{)}^2+(0-2{)}^2<9$

$5<9$ True

$(x-1{)}^2+(y-2{)}^2<9$

$0+0<2$ True

$x+y<2$

$y<-x+2$