8A F11 Q5

Question: Graph the system of inequalities $y<\vert x\vert +1$           $x^{2}+y^{2}\leq 9$

Foundations
1) What do the graphs of $y=\vert x\vert +1$, and $x^{2}+y^{2}=9$ look like?
2) Each graph splits the plane into two regions. Which one do you want to shade?
Answer:
1) The first graph looks like a V with the vertex at (0, 1), the latter is a circle centered at the origin with radius 3.
2) Since the Y-value must be less than $\vert x\vert +1$, shade below the V. For the circle shde the inside.

Solution:

Step 1:
The zeros of the left hand side are $-{\frac {1}{2}}$, 1, and 4