document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=40558>Question 40558</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534493947/algebrahomeworkh>INTERMEDIATE ALGEBRA</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 5.  Solve the system of equations using the addition (elimination) method.<BR>\n" );
document.write( "If the answer is a unique solution, present it as an ordered pair: (x, y).  If not, specify whether the answer is “no solution” or “infinitely many solutions.”<BR>\n" );
document.write( "6x + 2y = 2<BR>\n" );
document.write( "3x + 5y = 5<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #26015 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=26015\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve this system of equations using the elimination method.<BR>\n" );
document.write( "6x + 2y = 2<BR>\n" );
document.write( "3x + 5y = 5<BR>\n" );
document.write( "First we need to decide which coefficiant to work with in order to cancel out or \"eliminate\" the other.<BR>\n" );
document.write( "For instance, we have 6x and 3x.<BR>\n" );
document.write( "What do we need to do to the 3x in order to cancel out the 6x?<BR>\n" );
document.write( "What if we multiply the second (bottom) equation by -2. <BR>\n" );
document.write( "6x + 2y = 2<BR>\n" );
document.write( "-2(3x + 5y = 5)<BR>\n" );
document.write( "When we distribute, we get...<BR>\n" );
document.write( "6x + 2y = 2<BR>\n" );
document.write( "-6x -10y = -10<BR>\n" );
document.write( "Now we can add our system and eliminate the x (for now) and solve the equation for y. Like so...<BR>\n" );
document.write( "6x + 2y = 2<BR>\n" );
document.write( "-6x -10y = -10<BR>\n" );
document.write( "_______________<BR>\n" );
document.write( "0 - 8y = -8<BR>\n" );
document.write( "or...<BR>\n" );
document.write( "-8y = -8<BR>\n" );
document.write( "We can now divide both sides by -8...<BR>\n" );
document.write( "-8/-8 = 1<BR>\n" );
document.write( "So...<BR>\n" );
document.write( "y = 1<BR>\n" );
document.write( "But wait, we're not done yet!<BR>\n" );
document.write( "Now we have to insert the value for y into one of the original equations in order to get the value for x.<BR>\n" );
document.write( "So, let's take...<BR>\n" );
document.write( "6x + 2y = 2<BR>\n" );
document.write( "Insert the value for y = 1.<BR>\n" );
document.write( "6x + 2(1) = 2<BR>\n" );
document.write( "Now solve for x...<BR>\n" );
document.write( "6x + 2 = 2<BR>\n" );
document.write( "6x = 0<BR>\n" );
document.write( "if we divide both sodes by 6 we get 0/6 which equals 0<BR>\n" );
document.write( "So...<BR>\n" );
document.write( "x = 0 <BR>\n" );
document.write( "Now we should check to see if our answers make the original equations true<BR>\n" );
document.write( "6x + 2y = 2<BR>\n" );
document.write( "3x + 5y = 5<BR>\n" );
document.write( "or...<BR>\n" );
document.write( "6(0) + 2(1) = 2<BR>\n" );
document.write( "3(0) + 5(1) = 5<BR>\n" );
document.write( "These are both true.<BR>\n" );
document.write( "So our solution set is...<BR>\n" );
document.write( "(0,1)<BR>\n" );
document.write( "I hope this helps<BR>\n" );
document.write( "Good Luck! <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );