5 Key Points to Remember for Simultaneous Linear Equations using the Elimination Method
1. I have seen many students asking me whether to add or subtract in the Elimination Method. Let us first watch the video and then try to answer the question.
So, we see that we add the two equations when the signs of the terms containing the variable (to be eliminated), are different in the two given equations. But, if the two terms of the two equations, containing the same variable, have the same sign, then we have to subtract the two equations, which in turn means that we have to change the signs of every term of the second equation and then add the two equations.
2. Many times, students do not know which variable to be eliminated. You can eliminate any of the two variables, but there may be times when, eliminating one variable can be easier than eliminating the other. Let us take up three special cases one by one.
a). We have our previous video showing one variable with same sign and the other with opposite sign.
There is no harm if you eliminate ‘x’ instead of ‘y’, but in that case you have to subtract, which will require changing of sign of every term of the second equation and then adding. This would require a little bit of extra time and would also increase the chance of making careless mistakes in the whole process.
Therefore, always try to eliminate the variable having opposite signs in the two equations (if such a situation exists).
b).
You can eliminate ‘y’ as well, but then you have to multiply all the terms of both the equations with suitable numbers. So, you lose some time (during examination, this is crucial) and you gain some chances of making careless mistakes.
Therefore, always try to eliminate the variable having a coefficient of 1 in at least one of the two given equations (if such a situation exists).
c).
Again, in this case, we have chosen the variable ‘y’ to be eliminated because we have to multiply the terms of only one equation in order to get same coefficients for ‘y’ in both equations.
Therefore, always try to eliminate the variable having the coefficients as multiples of each other in the two equations (if such a situation exists).
3. Once, I had been asked by a student ‘Can we multiply by smaller numbers?’ Let us watch the video to find its answer.
Therefore, always multiply the two equations with the L.C.M. of the coefficients of the variable (to be eliminated) present in the two equations.
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