3x + 2y = 5; 2x - 3y = 7. Hence, the given lines are intersecting. So, the given pair of linear equations has exactly one solution and therefore it is consistent.
If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.
If a system has no solution, it is said to be inconsistent . Represent parallel lines.
if Both line slope are same and parallel to each other.
So, no solution
System is inconsistent.
if Both equation represent the same line. So, infinite many solution.
System is consistent.
if Both lines are parallel. So, no solution.
System is inconsistent.
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