Question

Solve by Substitution Show Steps x = −5y + 4z + 1 x − 2y + 3z = 1 2x + 3y − z = 2

Answer 1

Answer:

  (x, y, z) = (1-z, z, z) . . . . . . . an infinite number of solutions

Step-by-step explanation:

Use the first equation to substitute for x in the remaining two equations.

  (-5y +4z +1) -2y +3z = 1 . . . . substitute for x in the second equation

  -7y +7z = 0 . . . . . . . . . . . . . . simplify, subtract 1

  y = z . . . . . . . . . . . . . . . . . . . . divide by -7; add z

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  2(-5y +4z +1) +3y -z = 2 . . . . substitute for x in the third equation

  -7y +7z = 0 . . . . . . . . . . . . . . subtract 2; collect terms

  y = z . . . . . . . . . . . . . . . . . . . . divide by -7; add z

This is a dependent set of equations, so has an infinite number of solutions. Effectively, they are ...

  x = 1 -z

  y = z

  z is a "free variable"