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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.
`=> ab=-24 , a!=27/c and b!=(-8c)/9`
`=>` a and b have an infinite number of values.
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