Answer:
See attachment.
Step-by-step explanation:
Given system of inequalities:
[tex]\begin{cases} x > -1\\y > -3\\x+y < 2\\-2x+y < 4\end{cases}[/tex]
Rearrange the third and fourth inequalities to isolate y:
[tex]\implies y < 2-x[/tex]
[tex]\implies y < 2x+4[/tex]
When graphing inequalities:
- < or > : dashed line.
- ≤ or ≥ : solid line.
- < or ≤ : shade under the line.
- > or ≥ : shade above the line.
Graph the lines:
Draw the dashed line x = -1 and shade above the line (to the right).
Draw the dashed line y = -3 and shade above the line.
Draw the dashed line y = 2 - x and shade below the line.
Draw the dashed line y = 2x + 4 and shade below the line.
Therefore, the only graph that represents the given constraints is the second graph. (See attachment).
