Questions: The figure shows the healthy weight region for various heights for people ages 35 and older. If x represents height, in inches, and y represents weight, in pounds, the healthy weight region can be modeled by the system of linear inequalities below. Using this information, show that point A is a solution of the system of inequalities that describes healthy weight for this age group. 5.3 x - y ≥ 182 4.2 x - y ≤ 141 Substitute the x - and y-coordinates of point A for x and y in the first inequality. 194.2 ≥ 182

The figure shows the healthy weight region for various heights for people ages 35 and older. If x represents height, in inches, and y represents weight, in pounds, the healthy weight region can be modeled by the system of linear inequalities below. Using this information, show that point A is a solution of the system of inequalities that describes healthy weight for this age group. 5.3 x - y ≥ 182 4.2 x - y ≤ 141 Substitute the x - and y-coordinates of point A for x and y in the first inequality. 194.2 ≥ 182
Transcript text: The figure shows the healthy weight region for various heights for people ages 35 and older. If x represents height, in inches, and $y$ represents weight, in pounds, the healthy weight region can be modeled by the system of linear inequalities below. Using this information, show that point $A$ is a solution of the system of inequalities that describes healthy weight for this age group. \[ \left\{\begin{array}{l} 5.3 x-y \geq 182 \\ 4.2 x-y \leq 141 \end{array}\right. \] Substitute the $x$ - and $y$-coordinates of point $A$ for $x$ and $y$ in the first inequality. \[ 194.2 \geq 182 \]
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Solution

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Solution Steps

Step 1: Find the coordinates of point A.

Point A is located at (64, 150), where x=64 and y=150.

Step 2: Substitute the coordinates of point A into the first inequality.

5.3 * 64 - 150 ≥ 182 339.2 - 150 ≥ 182 189.2 ≥ 182 This inequality is true.

Step 3: Substitute the coordinates of point A into the second inequality.

4.2 * 64 - 150 ≤ 141 268.8 - 150 ≤ 141 118.8 ≤ 141 This inequality is true.

Final Answer

Since both inequalities are true when the coordinates of point A are substituted, point A is a solution to the system of inequalities. The first inequality simplifies to 189.2 ≥ 182.

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