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?
Given the system:
y = 6x - b
-3x + (1/2)y = -3
Options for 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 ensure that the two equations in the system are actually the same line.
The given equations are:
− 3 x + 2 1 y = − 3
y = 6 x − b
First, we will rewrite the first equation in the slope-intercept form y = m x + c :
− 3 x + 2 1 y = − 3
Multiply the entire equation by 2 to get rid of the fraction:
− 6 x + y = − 6
Now, solve for y :
y = 6 x − 6
Comparing this new form y = 6 x − 6 with the second equation y = 6 x − b , we see that both lines will have the same slope and y-intercept if b = 6 .
Therefore, the value of b that causes the system to have an infinite number of solutions is 6 .
Among the given options, the correct choice is 6 .
