SIMULTANEOUS LINEAR EQUATIONS

Introduction
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If two equations have the same variables and the same solutions then they are simultaneous linear equations. In general two simultaneous linear equation is,
a 1 x+ b 1 y= c 1 a 2 x+ b 2 y= c 2 MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIjxAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGabiGaaiaabeqaamaaeaqbaaGceaqabeaacaWGHbWaaSbaaSqaaiaaigdaaeqaaOGaamiEaiabgUcaRiaadkgadaWgaaWcbaGaaGymaaqabaGccaWG5bGaeyypa0Jaam4yamaaBaaaleaacaaIXaaabeaaaOqaaiaadggadaWgaaWcbaGaaGOmaaqabaGccaWG4bGaey4kaSIaamOyamaaBaaaleaacaaIYaaabeaakiaadMhacqGH9aqpcaWGJbWaaSbaaSqaaiaaikdaaeqaaaaaaa@4B81@






Examples of simultaneous linear equation
Table below shows three examples of linear equation whereby all of them are containing two variables.

x+2y=1 4x3y=18 MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIjxAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGabiGaaiaabeqaamaaeaqbaaGceaqabeaacaWG4bGaey4kaSIaaGOmaiaadMhacqGH9aqpcqGHsislcaaIXaaabaGaaGinaiaadIhacqGHsislcaaIZaGaamyEaiabg2da9iaaigdacaaI4aaaaaa@45DF@ 3m+4n=5 2m5n=12 MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIjxAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGabiGaaiaabeqaamaaeaqbaaGceaqabeaacaaIZaGaamyBaiabgUcaRiaaisdacaWGUbGaeyypa0JaaGynaaqaaiaaikdacaWGTbGaeyOeI0IaaGynaiaad6gacqGH9aqpcqGHsislcaaIXaGaaGOmaaaaaa@4670@ 7a2b=26 6a+5b=29 MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIjxAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGabiGaaiaabeqaamaaeaqbaaGceaqabeaacaaI3aGaamyyaiabgkHiTiaaikdacaWGIbGaeyypa0JaaGOmaiaaiAdaaeaacaaI2aGaamyyaiabgUcaRiaaiwdacaWGIbGaeyypa0JaaGOmaiaaiMdaaaaa@461E@

How to - Solving simultaneous linear equation?
There are several methods of solving simultaneous equations:
  1. Elimination Method
  2. Substitution Method
  3. By plotting graph
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