Answer:
Explanation:
The system of inequalities given is:
1. y ≤ x
2. y ≤ -x
To find the ordered pairs (x, y) that satisfy both inequalities, we need to determine the values of x and y that make both inequalities true.
Let's analyze each inequality separately:
1. y ≤ x:
This inequality states that y is less than or equal to x. This means that any ordered pair where y is less than or equal to x would satisfy this inequality. For example, if x = 5 and y = 3, this inequality is satisfied because 3 is less than 5.
2. y ≤ -x:
This inequality states that y is less than or equal to the negative of x. This means that any ordered pair where y is less than or equal to the negative of x would satisfy this inequality. For example, if x = 4 and y = -3, this inequality is satisfied because -3 is less than 4.
Now, let's consider the system of inequalities as a whole:
The ordered pairs (x, y) that satisfy both inequalities are those that satisfy both inequality 1 and inequality 2.
So, the solution to the system of inequalities y ≤ x and y ≤ -x would be the set of all ordered pairs (x, y) where y is less than or equal to x and y is also less than or equal to the negative of x.
In other words, any point below or on the line y = x and below or on the line y = -x would be a solution to the system of inequalities.
For example, the ordered pair (2, 2) satisfies both inequalities since 2 is less than or equal to 2 (y ≤ x) and 2 is less than or equal to -2 (y ≤ -x).
In summary, any ordered pair (x, y) that lies below or on the line y = x and below or on the line y = -x is a solution to the given system of inequalities.