Answer:
System a.
Step-by-step explanation:
Remember that the solution of a linear system of equations is shown by the interception point between those lines.
In this case, the interception point is at (2,3).
Also, the horizontal line is [tex]y=3[/tex]. Notice that the solution are is below this line, that means the inequality that represents that part is [tex]y\leq 3[/tex].
Now, the other line has y-intercept at -1, that means [tex]b=-1[/tex].
Then, we use two points (0,-1) and (2,3) to find its slope.
[tex]m=\frac{3-(-1)}{2-0}=\frac{4}{2}=2[/tex]
So, the equation that represents that line is [tex]y=2x-1[/tex].
Notice that the area of solution is above this line, that means the inequality is
[tex]y>2x-1[/tex]
Therefore, the sytem that represents the graph is
[tex]y>2x-1\\y\leq 3[/tex]
Notice that we used [tex]\leq[/tex] for the solid line and [tex]>[/tex] for the not solid line.
