Question

A. Select the two equations that represent this situation if x represents the age of the younger brother and y represents the age of the older brother.

(2 points)
Responses

x+y=6
𝑥
+
𝑦
=
6
x plus y is equal to 6

y=2+3x2
𝑦
=
2
+
3
𝑥
2
y is equal to 2 plus 3 x squared

y=6+x
𝑦
=
6
+
𝑥
y is equal to 6 plus x

y=2+3x
𝑦
=
2
+
3
𝑥

Answer 1

To select the two equations that represent the situation involving the ages of the younger brother \(x\) and the older brother \(y\), we can analyze each option:

1. **\(x + y = 6\)**: This equation could represent a situation where the total age of the two brothers is 6 years. This is a plausible equation.

2. **\(y = 2 + 3x^2\)**: This equation implies that the older brother's age is a function of the younger brother's age squared, which is unlikely in the context of simple age relationships.

3. **\(y = 6 + x\)**: This suggests that the older brother is 6 years older than the younger brother. If the younger brother is \(x\), then this relation makes sense.

4. **\(y = 2 + 3x\)**: This indicates that the older brother's age is 2 years plus 3 times the younger brother's age. This could also represent a reasonable age relationship, depending on how old they are.

Based on the interpretations:

- The viable equations representing the age relationship between the two brothers are **\(x + y = 6\)** and **\(y = 6 + x\)** if we view them as simple age relationships. However, **\(y = 2 + 3x\)** might also be possible if there's additional context about their ages.

Thus, the best two responses based on reasonable interpretations of family age differences would be:

- **\(x + y = 6\)**
- **\(y = 6 + x\)**

If you have additional information on their relationship, please provide it for more tailored options!