We have three methods.
1) Cramer's rule method (Or) Determinant method
2) Rank method
3) Matrix Inversion method.
see the text book of 12th standard mathematics in tamilnadu text book corporation.
My own question: For just 2 unknowns, do any of the above include the "ordinary" way in which you multiply one or the equations through so one of the unknowns match in both lines, subtract, solve the now-single difference for its unknown then substitute back? Or do the above only apply if you're solving great banks of equations simultaneously.
It's the only method I know but I recall being taught how to stretch it to 3 unknowns, but it becomes rather long-winded.
I ask out of curiosity because I "learnt" matrices without understanding them and with only the haziest hint that they have any uses!
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By the substitution method By the elimination method By plotting them on a graph
The analytical method involves simultaneous equations but if you do not know that, draw graphs of the equations: with one variable represented per axis. The solution, if any, is where the graphs meet.
Solve the following systems of simultaneous linear equations using Gauss elimination method and Gauss-Seidel Method 2x1+3x2+7x3 = 12 -----(1) x1-4x2+5x3 = 2 -----(2) 4x1+5x2-12x3= -3 ----(3) Answer: I'm not here to answer your university/college assignment questions. Please refer to the related question below and use the algorithm, which you should have in your notes anyway, to do the work yourself.
Without any equality signs the given terms can't be considered to be simultaneous equations.
it works exactly the same as it does with linear equations, you don't need to do any differentiation or anything fancy with this method, just have to plug in values of x, so it shouldn't make a difference if the equation is linear or nonlinear.