Question

select the correct answer.

given below is a system of equations.

\\
\

$$\begin{cases} 9x + 6y = b \\\\ 3x + 2y = 1 \\end{cases}$$

\\

which value of \\(b\\) results in infinitely many solutions for the system?

• 6
• 1
• 5
• 3

Explanation:

⚡ Using what you learned: introduction to systems of equations

Step 1: Analyze the condition for infinitely many solutions

For a system of linear equations to have infinitely many solutions, the two equations must represent the exact same line. This means one equation must be a direct multiple of the other.

Given system:

$$
LATEXBLOCK0
$$

Step 2: Find the scale factor

Compare the coefficients of \(x\) and \(y\) in both equations:

$$ \frac{9}{3} = 3 \quad \text{and} \quad \frac{6}{2} = 3 $$

The first equation is obtained by multiplying the second equation by a scale factor of \(3\).

Step 3: Solve for \(b\)

Multiply the constant term of the second equation by the same scale factor of \(3\):

$$ b = 1 \times 3 = 3 $$

Answer:

3