Final answer:
To graph the solution to the system of inequalities -7x+3y<-6 and -3x+4y<-4, we need to first graph the boundary lines of each inequality and determine the region that satisfies both inequalities. The correct answer is y<2x+2.
Step-by-step explanation:
To graph the solution to the system of inequalities -7x+3y<-6 and -3x+4y<-4, we need to first graph the boundary lines of each inequality. Then, we determine the region that satisfies both inequalities.
To graph the first inequality -7x+3y<-6, we can rewrite it as y>-rac{7}{3}x+2. This is in slope-intercept form y=mx+b, where m is the slope and b is the y-intercept. The slope is -rac{7}{3} , which means the line slopes downward to the right. The y-intercept is 2. So, we can start by plotting the point (0, 2) on the y-axis, and then use the slope to draw a line that passes through this point.
Similarly, we can rewrite the second inequality -3x+4y<-4 as y>rac{3}{4}x-1. This line also slopes downward to the right, but has a y-intercept of -1. So, we can plot the point (0, -1) on the y-axis, and then draw a line that passes through this point using the slope.
The region that satisfies both inequalities is the shaded region above the line y=-rac{7}{3}x+2 and above the line y=rac{3}{4}x-1. This means any point in this shaded region will satisfy both inequalities. Therefore, the correct answer is option d) y<2x+2.