A coordinate grid has a line labeled -3x + (1/2)y = -3 passing through the points (1, 0) and (0, -6).
What value of b will cause the system to have an infinite number of solutions?
The system is:
y = 6x - b
-3x + (1/2)y = -3
Possible values of b: 2, 4, 6, 8.
Answer (1)
To find the value of b that will cause the system to have an infinite number of solutions, we need to understand that this occurs when the two equations are, in fact, the same line.
The system of equations is:
y = 6 x − b
− 3 x + 2 1 y = − 3
Let's rewrite the second equation in the form of y = m x + c .
Starting with:
− 3 x + 2 1 y = − 3
Multiply everything by 2 to eliminate the fraction:
− 6 x + y = − 6
Now solve for y :
y = 6 x − 6
We can see the equation y = 6 x − 6 is of the same form as the first equation y = 6 x − b . For the two equations to represent the same line, b must equal 6.
Therefore, the value of b that will cause the system to have an infinite number of solutions is 6.
Thus, the correct option from the given choices is 6 .
