- If the system of equations has n variables with n-1 equations, then the solution is indeterminate
- If the system of equations has n variables with n-1 equations with some additional conditions like the variables are integers then the solution may be determinate
- If the system of equations has n variables with n-1 equations then some combination of variables may be determinable.
- For Example, if ax+by+cz=d and mx+ny+pz=q if a,b, and c are in Arithmetic progression and m,n and p are in AP then the sum x+y+z is determinable
- In questions, sometimes we are given information that can be written as ax + by + cz =d, ex + fy + gz = h, and we will be asked to find the value of lx + my + nz.
Here, the trick is to write lx + my + nz in terms of ax + by + cz and ex + fy + gz, for example: lx + my + nz = p( ax + by + cz) + q(ex + fy + gz) => lx + my + nz = p*d + q*h
Special Linear Equations
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