document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=55894>Question 55894</A>: <I><SPAN STYLE=\"word-break: break-all;\"> QUESTION: SOLVE THE SYTEM BY ADDITION\r<BR>\n" );
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document.write( "-5X+2Y=10<BR>\n" );
document.write( "X-3Y=11 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #37902 by </B><A HREF=/tutors/aboutme.mpl?userid=junior403><B>junior403(76)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=junior403><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=37902\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> SOLVE THE SYTEM BY ADDITION\r<BR>\n" );
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document.write( "-5X+2Y=10<BR>\n" );
document.write( "X-3Y=11\r<BR>\n" );
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document.write( "First we can add these equations vertically.<BR>\n" );
document.write( "-5X+2Y=10<BR>\n" );
document.write( "....X-3Y=11<BR>\n" );
document.write( "__________<BR>\n" );
document.write( "-4X-1Y=21<BR>\n" );
document.write( "Ok so far?<BR>\n" );
document.write( "Now we can solve this result for one of the variables. Lets choose Y.<BR>\n" );
document.write( "-4X-Y=21<BR>\n" );
document.write( "We can add 4X to both sides to move it to the right.<BR>\n" );
document.write( "-Y=21+4X<BR>\n" );
document.write( "Then we can divide each side of the equation by -1 to make the Y positive.<BR>\n" );
document.write( "Y=-21-4X<BR>\n" );
document.write( "Now that we have the value for Y we can insert that value into one of our original equations.<BR>\n" );
document.write( "X - 3(-21-4X) = 11<BR>\n" );
document.write( "Ok?<BR>\n" );
document.write( "Now we can solve for X.<BR>\n" );
document.write( "first we can distribute the -3 with everything inside the parentesis.<BR>\n" );
document.write( "X + 63 +12X = 11<BR>\n" );
document.write( "Then we can subtract 63 from both sides.<BR>\n" );
document.write( "X + 12X = -52<BR>\n" );
document.write( "Then we combine like terms.<BR>\n" );
document.write( "13X = -52<BR>\n" );
document.write( "Then we can divide both sides by 13.<BR>\n" );
document.write( "X = -4<BR>\n" );
document.write( "Now that we know the value of X, we can substitute the -4 in the other original equation.<BR>\n" );
document.write( "-5(-4)+2Y=10<BR>\n" );
document.write( "Distribute.<BR>\n" );
document.write( "20 + 2Y = 10<BR>\n" );
document.write( "Subtract 20 from both sides.<BR>\n" );
document.write( "2Y = -10<BR>\n" );
document.write( "Divide by 2.<BR>\n" );
document.write( "Y = -5<BR>\n" );
document.write( "So X = -4 and Y = -5<BR>\n" );
document.write( "To check this we can apply both results to one or both of the originals.<BR>\n" );
document.write( "-5X+2Y=10<BR>\n" );
document.write( "-5(-4)+2(-5)=10<BR>\n" );
document.write( "20 -10 = 10 TRUE<BR>\n" );
document.write( "X-3Y=11<BR>\n" );
document.write( "(-4)-3(-5)=11<BR>\n" );
document.write( "-4 + 15 = 11 TRUE<BR>\n" );
document.write( "I hope this helps.<BR>\n" );
document.write( "Good Luck!<BR>\n" );
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