Final answer:
To find ordered pairs that satisfy both inequalities y < 5x + 2 and y² < 2x + 1, a visual or algebraic approach is used. Ordered pairs that satisfy both conditions can be found by plotting the inequalities and looking for areas of overlap or by checking each pair algebraically. For instance, (1,2) satisfies the first inequality but fails to satisfy the second one.
Step-by-step explanation:
The student's question involves determining which ordered pairs satisfy two given inequalities: y < 5x + 2 and y² < 2x + 1. To find ordered pairs that satisfy both inequalities, we can use a process of substitution, graphical representation, or numerical testing. The process begins by plotting or identifying the region represented by each inequality on a coordinate plane. The region where the two inequalities overlap represents the set of ordered pairs that satisfy both inequalities. To check if a particular ordered pair meets the conditions of both inequalities, simply substitute the x and y values into each inequality and verify that the statements are true.
For example, let's consider the ordered pair (1,2). When we substitute these values into the first inequality, we get 2 < 5(1) + 2, which simplifies to 2 < 7. This is true. When we substitute the same ordered pair into the second inequality, we get (2)² < 2(1) + 1, which simplifies to 4 < 3. This is not true, so the ordered pair (1,2) does not satisfy both inequalities. This step-by-step approach can be applied to any list of ordered pairs to determine which ones meet the criteria of both inequalities.