Show that the following system of equations has an infinite number of solutions. x+y+2z = -2; 3x-y+14z=6; x+2y=-5
Substitute values of one equation into another.
(1) x+y+2z = -2; (2) 3x-y+14z=6; x+2y=-5 (3).
Substitute x in (1) and (2) from (3).
We get -y+2z=3 in (1).
We get -7y+14z=21 in (3).
Since (3) is (1)*7, we can conclude that the system has infinite solutions.
ES
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