Question

x + 5 = 3
y = 2x
COLUMN A: x
COLUMN B: y

• A. The quantity in Column A is greater.
• B. The quantity in Column B is greater.
• C. The two quantities are equal.
• D. The relationship cannot be determined from the information given.

Hint:

Be careful when comparing negative numbers. The number with the smaller absolute value is the greater number (e.g., -2 is greater than -10). Visualizing the numbers on a number line can help prevent mistakes.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
We are given a system of two linear equations with two variables, \(x\) and \(y\). We need to solve for \(x\) and \(y\) and then compare their values.
Step 2: Detailed Explanation:
First, solve the first equation for \(x\): \[ x+5 = 3 \] Subtract 5 from both sides: \[ x = 3 - 5 \] \[ x = -2 \] So, the quantity in Column A is -2. Next, use the value of \(x\) to find the value of \(y\) from the second equation: \[ y = 2x \] Substitute \(x = -2\): \[ y = 2(-2) \] \[ y = -4 \] So, the quantity in Column B is -4. Comparison:
We are comparing \(x = -2\) (Column A) with \(y = -4\) (Column B). On the number line, -2 is to the right of -4. Therefore, \( -2>-4 \). The quantity in Column A is greater.
Step 3: Final Answer:
By solving the system of equations, we find \(x=-2\) and \(y=-4\). Since \(-2>-4\), Column A is greater.