document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=969467>Question 969467</A>: <I><SPAN STYLE=\"word-break: break-all;\"> which of the following system of linear equation has an infinite number of solutions? please show work.\r<BR>\n" );
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document.write( "a. 2x+5y=1, 6x+15y=3<BR>\n" );
document.write( "b. x+y=10, x-y=4<BR>\n" );
document.write( "c. x+y=10, x-y=16<BR>\n" );
document.write( "d. x-2y=8, 2x+7y=-16 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #592350 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=592350\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An infinite number of solutions means the same equation.<BR>\n" );
document.write( "A is correct.<BR>\n" );
document.write( "2x+5y=1   Multiply each term by 3, and you get 6x+15y=3, which is the other equation.\r<BR>\n" );
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document.write( "The second one has a solution at x=7 and y=3.\r<BR>\n" );
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document.write( "The third one has a solution at x=13 and y=-3\r<BR>\n" );
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document.write( "The 4th one has a solution at x=8  y=0.\r<BR>\n" );
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document.write( "What you look for are multiples.  In A, I see 2x and 6x  That is a multiple of 3.  Then I look at y.<BR>\n" );
document.write( "5y and 15 y, also multiple of 3.  Then I look across the equals sign  1 and 3.  This is the same equation.  \r<BR>\n" );
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document.write( "Be careful, however.  If the second were 6x=15y +3, this is not a multiple, because the x and y are on opposite sides of the equals sign.  \r<BR>\n" );
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document.write( "x+y=something<BR>\n" );
document.write( "x-y = something  Almost always have a solution.  Just add the x s and the y s disappear.\r<BR>\n" );
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document.write( "2x + 5y=1<BR>\n" );
document.write( "6x+15y+3\r<BR>\n" );
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document.write( "Multiply top equation by 3   3{2x+5y=1)    3 * 2x=6x   3(5y)=15y   3*1=3   We distribute the 3 over every term in the equation\r<BR>\n" );
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document.write( "6x +15y=3<BR>\n" );
document.write( "6x +15y=3  (the bottom equation)\r<BR>\n" );
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document.write( "Multiply the top equation by (-1).  This changes all the signs.\r<BR>\n" );
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document.write( "-6x-15y=-3<BR>\n" );
document.write( "6x +15y =3   Now add<BR>\n" );
document.write( "0   + 0  = 0\r<BR>\n" );
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document.write( "This means that any x, y pair will work.  Both of these equations describe the same line.   I hope that helps!\r<BR>\n" );
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document.write( "I didn't show the solutions for the others, because the first one has an infinite number of solutions.  It can be shown that the others do not. </SPAN>\n" );
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