How do you solve this to graph the system of inequalities?
x+2y is equal to or less than 6
2x+y is equal to or less than 6
x is equal to or greater than 0
y is equal to or greater than 0
To graph the system of inequalities, you can follow these steps:
1. Start by graphing the equations x + 2y = 6 and 2x + y = 6 as if they were equalities.
2. To graph x + 2y = 6, first rearrange the equation to solve for y: y = (6 - x) / 2. Then choose some x-values and substitute them into the equation to find the corresponding y-values. Plot these points on the graph and connect them to form a straight line.
3. Similarly, for 2x + y = 6, solve for y: y = 6 - 2x. Choose different x-values, substitute them into the equation, and plot the corresponding y-values. Connect the points to form another straight line.
4. Now, to determine the solution region, you need to look at the inequalities. For x + 2y ≤ 6, you can shade the region below the line formed by x + 2y = 6. This is because any point below the line will satisfy the inequality.
5. Similarly, for 2x + y ≤ 6, shade the region below the line formed by 2x + y = 6.
6. Finally, to satisfy the conditions x ≥ 0 and y ≥ 0, shade the region that is to the right of the y-axis and above the x-axis.
7. The solution region is the overlapping shaded region that satisfies all the given inequalities.
Remember to check the boundary lines and make them either solid or dashed depending on whether the inequality is "less than or equal to" or "greater than or equal to."
In this case, the solution region will be the quadrilateral formed by the overlapping shaded regions.
I hope this explanation helps you graph the system of inequalities!