How many solutions does the system of equations #7x - 10y = 3# and #14x - 20y = 6# have?

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Answer 1 · 2017-06-09T21:17:20

An infinite number

Given:

#{(7x-10y=3),(14x-20y=6):}#

Notice that the second equation is just the first equation multiplied by #2#.

So these equations represent the same line, resulting in an infinite number of solutions.

graph{7x-10y=3 [-5, 5, -2.5, 2.5]}

#color(white)()#
Footnote

If you want to be precise, the number of solutions is c# = 2^omega#, the same uncountable cardinal number as the number of real numbers.