Question

HELP ASAP PLEASE!

Which graph represents the solution to this system of inequalities:
3x - 5y ≤ 15
y > -2/3 x + 1

Answer 1

To find the graph that represents the solution to the given system of inequalities, graph each inequality separately and find the overlapping region.

Step-by-step explanation:

To find the graph that represents the solution to the given system of inequalities, we need to graph each inequality separately and then find the region that satisfies both conditions.

Graph the first inequality, 3x - 5y ≤ 15, by replacing the inequality sign with an equal sign and shading the region below the line. This includes the line itself since it is a ≤ inequality.

Next, graph the second inequality, y > -2/3x + 1, by replacing the inequality sign with an equal sign and shading the region above the line. This does not include the line itself since it is a strict inequality. Finally, find the overlapping region of both inequalities to determine the solution graph. It should be the shaded area below the first line and above the second line.

Answer 2

1. You can add 5Y to both sides of the equation: 3X-5Y+5Y=5Y+15.

2. Subtract 15 from both sides to isolate "5Y." 3X-15=5Y.

3. Now, divide "5Y" by the number next to it. (3/5)X-15/5 =(5/5) Y.

4. Then simplify, and you get (3/5)X - 3 =Y. Enter this equation into the graphing calculator.

5. After you have both equations entered, press "GRAPH."

6. If you want to see the intersection of the two lines a little better, go to function 2, "WINDOW."

7. Change the X-min to X-min=-20 and Y-min=-15; then press "GRAPH" again.

8. To find the "intersect" button, go to 4th function called "TRACE." "Intersect" is number 5 on the list.

9. When you press it, it is asking for a guess, but all you need to do is press the "ENTER" button three times. You will see the word "Intersection." The two lines intersect at those X and Y values. Just write it into a coordinate point.

Note: This intersection point is the same for both lines. It is the solution to this system of equations. Check this out in the table function, which is right below the "GRAPH" function. Just press the "2nd" button on the left, right below the "Y=" button.

Go to the "X=-10" and Y1 and Y2= same values.

10. I am going to let you find the complete values for the coordinate point.