Final answer:
Benjamin may have made mistakes by incorrectly calculating intercepts or slopes, using dashed lines instead of solid lines, or shading the areas incorrectly for the system of inequalities 4x+7y≥26 and -5x+11y ≥ 7.
Step-by-step explanation:
When graphing the system of inequalities 4x+7y≥26 and -5x+11y ≥ 7, it is crucial to first identify the intercepts and then use the slope to graph the lines accurately. For the first inequality, the intercepts are found by setting each variable to zero in turn. Setting x to zero gives the y-intercept (0, 26/7), and setting y to zero gives the x-intercept (26/4, 0). The slope can be determined by rearranging the inequality to slope-intercept form, y = mx + b, which for this line would be y = -(4/7)x + (26/7). The line should then be graphed with a solid border because the inequality includes the case where 4x + 7y equals 26, and the area above the line should be shaded to represent the 'greater than' portion of the inequality.
For the second inequality, -5x + 11y ≥ 7, similar steps are followed. The x-intercept is (7/5, 0), and the y-intercept is (0, 7/11). After finding the slope from the rearranged inequality y = (5/11)x + (7/11), the line is graphed with a solid border and the area above it shaded.