document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=149217>Question 149217</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2x + 5y = 2<BR>\n" );
document.write( "2x - 2y = -12<BR>\n" );
document.write( "I am completely stuck on how to go about doing this problem.<BR>\n" );
document.write( "I think that the Solutions x and y are always intergers between 5 and -5. <BR>\n" );
document.write( "I dont understand how to do the substitution.. im used to X or Y being alone with no other number.\r<BR>\n" );
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document.write( "x = ?<BR>\n" );
document.write( "Y = ? \r<BR>\n" );
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document.write( "If you could, please show me a few steps on How to get the answer<BR>\n" );
document.write( "to this problem.<BR>\n" );
document.write( "I would greatly appreciate your help <BR>\n" );
document.write( "Thank You, <BR>\n" );
document.write( "Kerry G </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109466 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=109466\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> G'day Kerry G., what you have here is a system of equations, in this case, two equations with two unknowns (x and y).<BR>\n" );
document.write( "There several methods for solving systems of equations, but the basic idea is to first eliminate one of the variables and solve for the other.  Then you substitute the solved variable into either one of the two equations to solve for the other variable...and it's not as formidable as sounds!<BR>\n" );
document.write( "Starting with the two given equations:<BR>\n" );
document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B5y+=+2 ALIGN=MIDDLE  ALT=\"2x%2B5y+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-2y+=+-12 ALIGN=MIDDLE  ALT=\"2x-2y+=+-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > It looks like you can eliminate the x variable by subtracting one equation from the other. Let's subtract equation 2) from equation 1).  (It doesn't much matter which equation you subtract from which, it will work anyway)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B5y+=+2 ALIGN=MIDDLE  ALT=\"2x%2B5y+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-2y+=+-12 ALIGN=MIDDLE  ALT=\"2x-2y+=+-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7y+=+14 ALIGN=MIDDLE  ALT=\"7y+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" > You can see that the x variable has been eliminated. Now solve for y by dividing both sides of this equation by 7.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2 ALIGN=MIDDLE  ALT=\"y+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now that you have the value of y, you substitute this into either one of the two given equations to solve for x. Let's use equation 1).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B5y+=+2 ALIGN=MIDDLE  ALT=\"2x%2B5y+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute y = 2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B5%282%29+=+2 ALIGN=MIDDLE  ALT=\"2x%2B5%282%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B10+=+2 ALIGN=MIDDLE  ALT=\"2x%2B10+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 10 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+=+-8 ALIGN=MIDDLE  ALT=\"2x+=+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Finally, divide both sides by 2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-4 ALIGN=MIDDLE  ALT=\"x+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the solution is (-4, 2)<BR>\n" );
document.write( "What this means is that if you were to graph the given two linear equations, you would see two lines that intersect, and the point at which they intersect is the \"solution\" to the system of equations.<BR>\n" );
document.write( "Of course, graphing the two equations is another method of solving.<BR>\n" );
document.write( "Let's look at the graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C5%2C-5%2C5%2C%28-2%2F5%29x%2B2%2F5%2Cx%2B6%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C5%2C-5%2C5%2C%28-2%2F5%29x%2B2%2F5%2Cx%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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