document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=50291>Question 50291</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0073016020/algebrahomeworkh>Beginning Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to solve the following system by using addition or substitution. If a unique solution does not exist, state whether the system is dependent or inconsistent. \r<BR>\n" );
document.write( "\n" );
document.write( "I am unable to work this out. Can someone please help me?\r<BR>\n" );
document.write( "\n" );
document.write( "10x+2y=7<BR>\n" );
document.write( "y=-5x+3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #33459 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=33459\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 10x+2y=7<BR>\n" );
document.write( "y=-5x+3\r<BR>\n" );
document.write( "\n" );
document.write( "We can solve this system of equations using the elimination method.<BR>\n" );
document.write( "But first we need to put each equation in standard form so that they look the same. You have...<BR>\n" );
document.write( "10x + 2y = 7<BR>\n" );
document.write( "y  = -5x + 3<BR>\n" );
document.write( "The top equation is already in standard form so we just need to get the -5x in the bottom equation on the left side by adding it from both sides.<BR>\n" );
document.write( "10x + 2y = 7<BR>\n" );
document.write( "5x  + y  = 3<BR>\n" );
document.write( "Now we are ready to begin eliminating variables.\r<BR>\n" );
document.write( "\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 10x and 5x.<BR>\n" );
document.write( "What do we need to do to the 5x in order to cancel out the 10x?<BR>\n" );
document.write( "What if we multiply the second (bottom) equation by -2? <BR>\n" );
document.write( "10x  + 2y = 7<BR>\n" );
document.write( "-2(5x + y = 3)<BR>\n" );
document.write( "When we distribute, we get...<BR>\n" );
document.write( "10x  + 2y = 7<BR>\n" );
document.write( "-10x - 2y = -6<BR>\n" );
document.write( "Now we can add our system to solve the equation. Like so...<BR>\n" );
document.write( "10x  + 2y = 7<BR>\n" );
document.write( "-10x - 2y = -6<BR>\n" );
document.write( "_______________<BR>\n" );
document.write( "0  =  1\r<BR>\n" );
document.write( "\n" );
document.write( "Is this statement true 0 = 1?<BR>\n" );
document.write( "NO!<BR>\n" );
document.write( "So the solution is inconsistent.<BR>\n" );
document.write( "We can write the answer as...<BR>\n" );
document.write( "zero, 0 or empty set, { }.\r<BR>\n" );
document.write( "\n" );
document.write( "I hope this helps.<BR>\n" );
document.write( "Good Luck!\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );