document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=552106>Question 552106</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with this problem. :\r<BR>\n" );
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document.write( "Select any two integers between -12 and +12 which will become solutions to a system of two equations.<BR>\n" );
document.write( "Write two equations that have your two integers as solutions. Show how you built the equations using your integers<BR>\n" );
document.write( "Solve your system of equations by the addition/subtraction method. Make sure you show the necessary 5 steps. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #360099 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=360099\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let's take 2 integers at random.<BR>\n" );
document.write( "we'll use -3 and 9<BR>\n" );
document.write( "we'll let x = -3 and y = 9<BR>\n" );
document.write( "let's take one equation at random.<BR>\n" );
document.write( "we'll take 5x + 6y = z<BR>\n" );
document.write( "when x = -3 and y = 9, this equation becomes:<BR>\n" );
document.write( "5(-3) + 6*9 = z which results in:<BR>\n" );
document.write( "z = 39<BR>\n" );
document.write( "our first equation becomes:<BR>\n" );
document.write( "5x + 6y = 39<BR>\n" );
document.write( "now lets take any other equation at random.<BR>\n" );
document.write( "let's try -15x - 30y = z<BR>\n" );
document.write( "when x = -3 and y = 9, this equation becomes:<BR>\n" );
document.write( "-15x - 30y = -225<BR>\n" );
document.write( "we now have 2 equation that can be solved simultaneously.<BR>\n" );
document.write( "they are:<BR>\n" );
document.write( "5x + 6y = 39<BR>\n" );
document.write( "-15x - 30y = -225<BR>\n" );
document.write( "if we did this right, then solution should be x = -3 and y = 9.<BR>\n" );
document.write( "let's see how we did.<BR>\n" );
document.write( "if we multiply the first equation by 3, we get:<BR>\n" );
document.write( "15x + 18y = 117 (first equation multiplied by 3)<BR>\n" );
document.write( "-15x - 30y = -225 (second equation)<BR>\n" );
document.write( "if we add both these equations together, we get:<BR>\n" );
document.write( "-12y = -108<BR>\n" );
document.write( "if we divide both sides of this equation by -12, we get:<BR>\n" );
document.write( "y = 9<BR>\n" );
document.write( "so far so good.<BR>\n" );
document.write( "we go back to the original equations of:<BR>\n" );
document.write( "5x + 6y = 39 (first equation)<BR>\n" );
document.write( "-15x - 30y = -225 (second equation)<BR>\n" );
document.write( "substituting 9 for y in the first equation gets:<BR>\n" );
document.write( "5x + 54 = 39<BR>\n" );
document.write( "solving for x in the first equation get:<BR>\n" );
document.write( "x = -3<BR>\n" );
document.write( "substituting 9 for y and -3 for x in the second equation gets:<BR>\n" );
document.write( "-15(-3) - 30(9) = -225 which becomes:<BR>\n" );
document.write( "45 - 270 = -225 which becomes:<BR>\n" );
document.write( "-225 = -225<BR>\n" );
document.write( "this confirms the values of x = -3 and y = 9 is a solution to both equations.<BR>\n" );
document.write( " </SPAN>\n" );
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