A system of equation is said to be consistent if it has at least one solution.
If a consistent system has an infinite number of solutions, it is dependent.
Given the system of the equation:
[tex]\begin{gathered} y=3x+5 \\ y=ax+b \end{gathered}[/tex]For the system to be dependent and consistent, they must be the same line.
Therefore, the values for a and b that make the system consistent and dependent are:
a=3, b=5
A system is said to be inconsistent if it has no solution. That is, the two lines do not intersect (are parallel).
Therefore, the values of a and b that make the system inconsistent are:
a=3, b= -5
