- When we attempt to solve the following two-by-two linear system, we will fail. Try it
using the double-elimination method and see what happens. Here are the equations:
2 x+y= 3
and
6 x+ 3 y= 12Is something wrong with one or both of these equations? Why can’t we solve this
system?
- Put the two original equations from Prob. 5 into SI form. What does this tell us about
their graphs? Would drawing the graphs provide any clues about why the system can’t
be solved? - Look again at the general derivation for solving a two-by-two system by double
elimination. Remember the “taboo” concerning the constants. Does this have anything
to do with why the system described in Probs. 5 and 6 can’t be solved? Plug in the
numbers and see what happens. - Solve the two-by-two linear system given in Prob. 1 using the rename-and-replace
(substitution) method. - Solve the two-by-two linear system given in Prob. 4 using the rename-and-replace
method. - Attempt to solve the following pair of equations as a two-by-two linear system by
substitution. You’ll get a meaningless result. Why?
s= 2 r− 3
and
− 10 r+ 5 s+ 15 = 0Practice Exercises 263