- Derive a two-by-two linear system in x and y from the solution to Prob. 1, along
with the equation in x and y that we derived from the second and third three-variable
equations in the section “Eliminate One Variable.” - Solve the two-by-two linear system obtained in the solution to Prob. 2. Use the double-
elimination method. - Solve for z by substituting the values for x and y (solution 3) into the first equation
stated in Prob. 1. - Derive a two-by-two linear system in x and y from the solution to Prob. 1, along with
the equation in x and y that we derived from the first two three-variable equations in
the section “Eliminate One Variable.” - Solve the two-by-two linear system obtained in the solution to Prob. 5. Use the morph-
and-mix method, treating y as the independent variable and x as the dependent variable. - Solve for z by substituting the values for x and y (solution 6) into the second equation
stated in Prob. 1. - The following four-by-two linear system has a unique solution, even though there are
more equations than variables. How can we know this without doing any algebra or
graphing the equations? What is that solution?
y=−x+ 1
y=− 2 x+ 1
y= 3 x+ 1
y= 4 x+ 1
- Plug in the values for x and y that appear to solve the set of equations in Prob. 8, based
on the reasoning in the solution to Prob. 8. Verify that these values satisfy all four
equations. - Graph all four of the lines presented in Prob. 8. On the basis of this graph, explain why
any pair or triplet of these equations, taken as a two-by-two or three-by-two system, has
the same unique solution as any other pair or triplet of the equations.
Practice Exercises 295