Question

Given below is a system of equations.

9x + 6y = b
3x + 2y = 1
Which value of b results in infinitely many solutions for the system?

A) b = 0
B) b = 3
C) b = 6
D) b = 9

Answer 1

The value of b that results in infinitely many solutions for the system of equations is b = 3, as with this value, both equations represent the same line.

Step-by-step explanation:

The question involves finding a specific value of b that results in a system of equations having infinitely many solutions. To determine this, we analyze the two equations provided:

• 9x + 6y = b
• 3x + 2y = 1

For the system to have infinitely many solutions, both equations must represent the same line, meaning they must be proportional. We can see that the second equation can be multiplied by 3 to potentially match the first:

• (3x + 2y) * 3 = 3 * 1
• 9x + 6y = 3

Now we see that if b equals 3, the two equations are identical, which would lead to infinitely many solutions. Therefore, the correct answer is b = 3.