# The system of equations 3x + by + c = 0 and ax - 8y + 9 = 0 does not have any solution. What are the possible values of a and b.

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Each of the equations in the given system of equations represents a straight line. The solution of the system of equations is the point at which the lines intersect.

The system of equations does not have a solution if the two lines are parallel to each other. They can be expressed in the slope intercept form as follows:

3x + by + c = 0

=> `y = (-3/b)x - c/b`

ax - 8y + 9 = 0

=> `y = (a/8)x + 9/8`

The slope of the lines is equal if `-3/b = a/8 => a*b = -24` .

**a and b can take on an infinite number of values for which the given equations do not have a solution. The product a*b should be equal to -24.**

The system of equations 3x + by + c = 0 and ax - 8y + 9 = 0 does not have any solution.

`=> 3/a=b/(-8)!=c/9`

`=> ab=-24 , a!=27/c and b!=(-8c)/9`

`=>` a and b have an infinite number of values.