We can find out about the solutions of the system by comparing the solutions to certain rules that are explained below.
Let's consider a system of two linear equations with two unknown variables:
Ax+By = C
Dx+Ey = F
Here, we include a number K such that D = KA and E = KB.
One of the best methods to check the solutions is by graphing them but we are not allowed to use those in this question. In order to find out about the conditions, we use the following rules -
(i) If it has no solutions - F is not equal to KB.
(ii) If it has one and only one solution - If the system contains no linear dependency between equations, then it has only one solution.
(iii) If it has infinitely many solutions - F is equal to KB.
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