Algebra-1

The relationship between a system of inequalities and its graph on the coordinate plane is as follows:

The solution set of a system of inequalities can be represented as a region on the coordinate plane. Each inequality corresponds to a boundary line on the plane, which divides the plane into two parts. Depending on the inequality symbol (greater than or less than), the solution set lies on one side of the boundary line.

For this question, we need to find the function of 2 intersecting lines,
First these 2 functions must be y = kx + b cause they are linear functions. By observing their intersections with the x and y axes, we can determine:
①Through(3, 0) and (0, -3), they are 2 solutions for y = kx + b.
Put them into y = kx + b, thus we got
0 = 3*k + b
-3 = 0*k + b
Through the second equation we got b = -3
Put b = -3 into 0 = 3*k + b we got
k = 1
Thus, the equation is y = x - 3

②Use the same way to solve the dash line function, it goes through(0, 3) and (2, -1)
Put them into y = kx + b, thus we got
3 = 0*k + b
-1 = 2k + b

Thus, b = 3. put it into -1 = 2k + b, so k = -2
Thus the equation is y = -2x + 3

The shaded region is above both functions, that means the value(y) should be bigger than both functions. Thus:
y > x - 3

Click "Show Answer" to reveal the answer and analysis