what is independent equation??
Answers
The term independent equation refers to the equation which is not in proportional with other equations. For better understanding come to the point of examples:
Take two pairs of equations;
1st pair includes:
2x+5y=36
5x-7y=28
2nd pair includes:
2n+5m=85
4n+10m=170
Now observe the equations, in the first pair we don't get any relationship, they are independent but in second par the first equation is in proportional with the second equation in the ratio 1:2, its showing a dependence or there is only one equation or they are equivalent to each other and both the equation is enough sufficient to explain the other equation. So, they are dependent but in the first pair there is no such case so, they are independent.
If a consistent system has exactly one solution, it is independent .
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 .