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Solving simultaneous equations using the different methods

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The percentage of households with a television tuned in to ad-supported cable increased linearly from 24.6% in 1995 to 42.5% in 2009. The percentage of households with a TV tuned into a major network decreased linearly from 47% in 1995 to 32% in 2009. Estimate when the percentages were equal for cable and the major networks.

Solution Preview

Let the time in years passed since 1995 be denoted by t, Let x denote the % of viewing cable households at any one time, let y denote the % of network viewing households at any one time.

A linear increase for cable viewers (in 1995 24.6%, in 2009 42.5%) gives rate of increase per year (m1) as computed below.

m1 = (42.5 - 24.6)/(2009 - 1995) = 17.9/15 % per yr

Let initial time since 1995 be t (t measured in years), ...

Solution Summary

4 questions are posed and simultaneous equations are solved using the graphical method, substitution and eliminations methods. The final question involves using word description to form word and simultaneous equations which are then solved