If ABC are positive numbers where a + b equal to 4 and b + 2 c equal to 5 then

Given the conditions:

1. \( a + b = 4 \)
2. \( b + 2c = 5 \)

Let's analyze and solve for \( a \), \( b \), and \( c \) under the assumption that \( a \), \( b \), and \( c \) are positive numbers.

### Step 1: Express \( a \) and \( c \) in terms of \( b \).

From the first equation:
\[ a = 4 - b \]

From the second equation:
\[ 2c = 5 - b \]
\[ c = \frac{5 - b}{2} \]

### Step 2: Ensure \( a > 0 \), \( b > 0 \), and \( c > 0 \).

For \( a > 0 \):
\[ 4 - b > 0 \Rightarrow b < 4 \]

For \( c > 0 \):
\[ \frac{5 - b}{2} > 0 \Rightarrow 5 - b > 0 \Rightarrow b < 5 \]

### Step 3: Determine the range for \( b \).

Since \( b \)

Learn how to solve a system of linear equations with two variables using an example problem. Given conditions: a + b = 4 and b + 2c = 5. Explore step-by-step solutions for finding the values of a, b, and c, ensuring all variables are positive. Suitable for students in Grades 7-9.

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