For Problems 14, refer to the following systems of equations:
I.

II.

III.

IV.

For which of these systems are the equations said to be dependent?
To find:
The dependent system of equations.
Graphing a system of two linear equation in two variables produces one of the following results.
1. The graphs of two equations are two intersecting lines, which indicates that there are one unique solution of the system. Such a system is called consistent system.
2. The graphs of the two equations are parallel lines, which indicate that there is no solution for the system. It is called an inconsistent system.
3. The graph of two equations are the same line, which indicates infinitely many solutions for the system. The equations are called dependent equations.
Calculation:
(I)
Let graph the lines by determining intercepts and a check point for each of the lines.
Solve the equation (1) for y we get,
Adding
Solve the equation (2) for y we get,
Adding
The graph of the given system is,
(II)
Let graph the lines by determining intercepts and a check point for each of the lines.
Solve the equation (1) for y we get,
Adding
Solve the equation (2) for y we get,
Adding
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