document.write( "Question 557217: without graphing determine the number of solutions of the following system of equations: 4x-10y=-5 and 2x-5y=0 \n" ); document.write( "

Algebra.Com's Answer #362501 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
(1) $\"+4x+-+10y+=+-5+\"$
\n" ); document.write( "(2) $\"+2x+-+5y+=+0+\"$
\n" ); document.write( "----------------
\n" ); document.write( "They are straight lines, so they must either:
\n" ); document.write( "(1) intersect at 1 point ( different slopes )
\n" ); document.write( "(2) Not intersect ( same slope )
\n" ); document.write( "(3) They are actually the same line
\n" ); document.write( "---------------------------
\n" ); document.write( "If I divide both sides of (1) by $\"2\"$ ,
\n" ); document.write( "I get
\n" ); document.write( "(1) $\"+2x+-+5y+=+-%285%2F2%29+\"$
\n" ); document.write( "(1) $\"+5y+=+2x+%2B+%285%2F2%29+\"$
\n" ); document.write( "(1) $\"+y+=+%282%2F5%29%2Ax+%2B+%281%2F2%29+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+2x+-+5y+=+0+\"$
\n" ); document.write( "(2) $\"+5y+=+2x+\"$
\n" ); document.write( "(2) $\"+y+=+%282%2F5%29%2Ax+\"$
\n" ); document.write( "----------------
\n" ); document.write( "The lines have the same slope, and they are not
\n" ); document.write( "the same line, so they must be parallel.
\n" ); document.write( "Parallel lines have no solution. \n" ); document.write( "

\n" );