document.write( "Question 74209: Find k if the following system of equations has infinite solutions
\n" ); document.write( "kx + 3y = k – 3
\n" ); document.write( "12x + ky = k
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #53316 by jim_thompson5910(35256) $\"\"$ $\"About$

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If we let k=6 then we get
\n" ); document.write( " $\"6x%2B3y=3\"$
\n" ); document.write( " $\"12x%2B6y=6\"$
\n" ); document.write( "Notice how the 2nd equation is just two times the first equation (ie $\"2%286x%2B3y%29=2%283%29\"$ becomes $\"12x%2B6y=6\"$ ) Since one equation is a multiple of the other and the system is dependent, there are infinite solutions. In other words, the two equations produce the same line, but one equation is just twice the other. \n" ); document.write( "

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