Question

The following system of inequalities shows the relationship between two numbers, where the value of x is less than the value of y, and both numbers are integers. two lines intercept the x and y-axis at 0.5, 1 unit and minus 3, minus 3 units. both intersect at (minus 0.7, 2.4) with a dark shaded region on the upper side, and lightly shaded on the left and right sides. Which solution is valid within the context of the situation?

1) (-1.5,4)
2) (-2,1)
3) (-1,5)
4) (1,4.5)

Answer 1

The only valid solution for the system of linear inequalities where x is less than y and both are integers, among the given options, is (-1, 5).

Step-by-step explanation:

The student's question involves determining a valid solution for a system of linear inequalities represented graphically. The inequalities have been described in terms of intercepts and slopes, and it is also said that the numbers x and y must satisfy x being less than y, with both x and y being integers. To find the correct pair (x, y), we need to assess which of the given pairs of integers satisfies the inequalities and the condition that x < y.

Looking at the options provided:
1) (-1.5, 4) does not satisfy the condition as x is not less than y.
2) (-2, 1) does not satisfy the condition as x is not less than y.
3) (-1, 5) satisfies both the inequalities and the condition x < y.
4) (1, 4.5) does not satisfy the condition as y is not an integer.

Therefore, the only valid solution is option 3) (-1, 5), where x is indeed less than y, and both values are integers.