Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.

Question

y < 6/5x -2

y > 1/5x + 5

Answer 1

Answer 2

Hi Elise F

Try the link below let me know if were able to access it.

https://www.desmos.com/calculator/k8szkd7aah

(15,10) exists within the overlap area but does not touch the dashed lines

When x is 15

(6/5)x -2 = (6/5)15 -2 = 18- 2 = 16 =y so y is greater than 10

(1/5)x +5 = (1/5)15 + 5 = 3+ 5 = 8 =y so y is less than 10

Hope this helps

Answer 3

To start, graph the two lines

y = 6/5x-2 (equation 1)

y=1/5x+5 (equation 2)

Starting with the inequality y<6/5x-2, we look at the line and pick a point on either side. I like to pick (0,0) because it makes the math easy. Plugging (0,0) into the inequality gives 0<-2. Since this is false, we know that the correct region is the one that does NOT include (0,0). So we shade that part of the graph.

Now, do the same for the other inequality. Plugging in (0,0) gives 0>5, so we take the side of the line that does not include (0,0)

The final solution is the area where both inequalities are true (where the blue and red regions overlap). Any point within that region is a solution

Let me know if this helps!