PROVE: Can a Linear System Have Exactly Two Solutions? (a) Suppose that (xo, Yor zo) and (x1, y1, 21) are solutions of the system ax + by + c,z = d, azx + bzy + C2z = d2 azx + bzy + C32 = dz (X + x Yo+ yi 20 + z1 2 2' 2 Show that is also a solution. (b) Use the result of part (a) to prove that if the system has two different solutions, then it has infinitely many solutions.

PROVE: Can a Linear System Have Exactly Two Solutions? (a) Suppose that (xo, Yor zo) and (x1, y1, 21) are solutions of the system ax + by + c,z = d, azx + bzy + C2z = d2 azx + bzy + C32 = dz (X + x Yo+ yi 20 + z1 2 2' 2 Show that is also a solution. (b) Use the result of part (a) to prove that if the system has two different solutions, then it has infinitely many solutions.

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter5: Systems Of Equations And Inequalities

Section5.2: Systems Of Linear Equations In Several Variables

Problem 49E

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Similar questions

Find a system of two equations in three variables, x1, x2 and x3 that has the solution set given by the parametric representation x1=t, x2=s and x3=3+st, where s and t are any real numbers. Then show that the solutions to the system can also be written as x1=3+st,x2=s and x3=t.
Consider the system of linear equations in x and y. ax+by=ecx+dy=f Under what conditions will the system have exactly one solution?

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