The Common Sense Computer
There is a computer that can perform one of the four basic operations every second(it take the same amount of time to perform 1+1 as it takes to perform 434344645x35464745). Given a system of 2x2 linear equations
ax + by = c nx+my = p
Which is faster: Substitution or Cramer's Rule? Express your answer as A+B where A is the time in seconds for substitution and B is the time for Cramer's Rule.
Note that splitting fractions takes 0 seconds and that dividing/multiplying by one is still 1 second.
The answer is 20.
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1 solution
The time for Cramers rule is 3 comps per det x3 dets + 2 divisons = 11 seconds. The time for substitution is 1(subtract by)+1(divide by a)+1(multiply by n)+1 (add my to (nb/a)y)+2(solve remaining two step equation)+1(multiply by b)+2 (solve remaining two step equation)=9.9+11=20.