Which graph represents the system of…

The system of inequalities can be expressed as: [tex]3x + 5y leq 10[/tex] ……….[1] and [tex]x – y < -1[/tex] ..........[2]. To graph each inequality, the line for [tex]x - y < -1[/tex] is dashed, indicating that points on this line are not included in the solution set, as depicted in Figure 1. The intercepts are determined by locating where the graph intersects the axes. The y-intercept for the equation related to inequality [2], which is [tex]x - y = -1[/tex], is found by setting x to 0: 0 - y = -1, resulting in y = 1, so the y-intercept is (0, 1). To find the x-intercept, we set y to 0 in the same equation: x - 0 = -1 gives x = -1, yielding the x-intercept at (-1, 0). For the second inequality [1], [tex]3x + 5y leq 10[/tex] is graphed with a solid line to signify that points on the line are included in the solution region, represented in Figure 2. The related equation is [tex]3x + 5y = 10[/tex]. Setting x to 0 for the y-intercept: 0 + 5y = 10 leads to y = 2, so the y-intercept is (0, 2). For the x-intercept, set y to 0: [tex]3x = 10[/tex] gives x ‚âà 3.33, making the x-intercept (3.33, 0). The solution to the system comprises the ordered pairs found in the area where the graphs of [tex]3x + 5y leq 10[/tex] and [tex]x - y < -1[/tex] overlap. Consequently, the darkest shaded region in Figure 3 represents the solution area, confirming that option D is the correct answer.