Question

puzzle #1
1 find graph 1s inequality.
2 find graph 2s inequality.
3 is ☆ a solution to the system?
4 is ♡ a solution to the system?
answer choices
a: yes
b: y>-x
c: y≤2x-3
d: y≤-x
e: y≥2x-3
f: no
g: y<2x-3
h: y<-x
i: y>2x-3
type the 4-letter code into the answer box. all caps, no spaces.
type in all caps with no spaces.
your answer

Explanation:

Step1: Identify Graph 1's inequality

First, Graph 1 (purple dashed line) has a slope of $-1$ and y-intercept $0$, so its base line is $y=-x$. The shaded region is above the dashed line, so the inequality is $y > -x$, which matches option B.

Step2: Identify Graph 2's inequality

Graph 2 (solid teal line) has a slope of $2$ and y-intercept $-3$, so its base line is $y=2x-3$. The shaded region is below the solid line, so the inequality is $y \leq 2x-3$, which matches option C.

Step3: Check star as system solution

The star ($\star$) is in the overlapping purple-teal region. Test its coordinates (e.g., $(3,2)$) in both inequalities:
$2 > -3$ (true) and $2 \leq 2(3)-3=3$ (true). So it is a solution, matching option A.

Step4: Check heart as system solution

The heart ($\heartsuit$) is not in the overlapping region. Test its coordinates (e.g., $(-2,1)$) in both inequalities:
$1 > 2$ (false, since $-(-2)=2$). So it is not a solution, matching option F.

Answer:

BCAF