document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=58035>Question 58035</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;\"> Can someone help me on ths problem?\r<BR>\n" );
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document.write( "  I need to solve the following systems by addition.  If a unique solution does not exist, I need to state whether the system is inconsistent or dependent.\r<BR>\n" );
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document.write( "  2x + 3y = 1<BR>\n" );
document.write( "  5x + 3y = 16\r<BR>\n" );
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document.write( " Thanks so much,<BR>\n" );
document.write( "  Sher </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #39685 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=39685\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi Sher,<BR>\n" );
document.write( "I need to solve the following systems by addition.  If a unique solution does not exist, I need to state whether the system is inconsistent or dependent.<BR>\n" );
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document.write( "L1)  2x + 3y = 1<BR>\n" );
document.write( "L2)  5x + 3y = 16<BR>\n" );
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document.write( "Multiply L2 by -1 and add it to L2 and the y's will be eliminated.<BR>\n" );
document.write( " -1(5x+3y)=-1(16) --->> -5x-3y=-16<BR>\n" );
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document.write( "2x +3y=1<BR>\n" );
document.write( "-5x-3y=-16<BR>\n" );
document.write( "____________<BR>\n" );
document.write( "-3x+0y=-15<BR>\n" );
document.write( "-3x=-15<BR>\n" );
document.write( "-3x/-3=-15/-3<BR>\n" );
document.write( "x=5  <BR>\n" );
document.write( "Substitute x=5 into L1 and solve for y:<BR>\n" );
document.write( "2(5)+3y=1<BR>\n" );
document.write( "10+3y=1<BR>\n" );
document.write( "-10+10+3y=1-10<BR>\n" );
document.write( "3y=-9<BR>\n" );
document.write( "3y/3=-9/3<BR>\n" );
document.write( "y=-3<BR>\n" );
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document.write( "The solution is (x,y)=(5,-3)<BR>\n" );
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document.write( "FYI, if you go to eliminate one variable and both variables get eliminated and you get two numbers that aren't equal like 4=5, then the system has no solution and is inconsistent.  If the same thing happens, but the numbers left do equal each other like 4=4, then the system has an infinite number of solutions and the system is dependent.<BR>\n" );
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document.write( "Happy Calculating, Sher. </SPAN>\n" );
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