Questions: 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. x - y ≤ -3 2x + y ≥ 1 Which solution is valid within the context of the situation? (-1,5)

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.

x - y ≤ -3
2x + y ≥ 1

Which solution is valid within the context of the situation?
(-1,5)

Transcript text: 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. \[ \begin{aligned} x-y & \leq-3 \\ 2 x+y & \geq 1 \end{aligned} \] Which solution is valid within the context of the situation? $(-1,5)$

Solution

Solution Steps

Step 1: Check (1,4)

Substituting x = 1 and y = 4 into the inequalities: 1 - 4 ≤ -3 => -3 ≤ -3 (True) 2(1) + 4 ≥ 1 => 6 ≥ 1 (True) Since x < y (1 < 4), this solution is valid.

Step 2: Check (-1.5, 4)

The problem states that x and y are integers. Since x = -1.5 is not an integer, this solution is invalid.

Step 3: Check (-2,1)

Substituting x = -2 and y = 1 into the inequalities: -2 - 1 ≤ -3 => -3 ≤ -3 (True) 2(-2) + 1 ≥ 1 => -3 ≥ 1 (False) Since the second inequality is false, this solution is invalid.

Final Answer

(1,4)

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