document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=70479>Question 70479</A>: <I><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "The solution of the system 4x+5y =2 and 6x-2y=b is (3,a). Find the values of a and b. \r<BR>\n" );
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document.write( "Helpp </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #50299 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=50299\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Start with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B5y=2 ALIGN=MIDDLE  ALT=\"4x%2B5y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The fact that the point (3,a) satisfies the system of equations (that means it satisfies both equations), tells you that when x = 3 and y = a, the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B5y+=+2 ALIGN=MIDDLE  ALT=\"4x%2B5y+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "is satisfied.  So plug in 3 for x and a for y.  When you do, the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A3+%2B+5%2Aa+=+2 ALIGN=MIDDLE  ALT=\"4%2A3+%2B+5%2Aa+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+%2B+5%2Aa+=+2 ALIGN=MIDDLE  ALT=\"12+%2B+5%2Aa+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract 12 from each side of this equation to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Aa+=+2-12+=+-10 ALIGN=MIDDLE  ALT=\"5%2Aa+=+2-12+=+-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally, divide both sides by 5 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-10%2F5+=+-2 ALIGN=MIDDLE  ALT=\"a+=+-10%2F5+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So now you know that a = -2 and that is one of the things you had to find.  You can substitute<BR>\n" );
document.write( "this into the point (3,a) which is known to work in both equations because it is the solution<BR>\n" );
document.write( "to the system of equations.  By substituting -2 for a you know that the point (3, -2) satisfies<BR>\n" );
document.write( "both equations.<BR>\n" );
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document.write( "The second equation of the system of equations is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x+-+2y+=+b ALIGN=MIDDLE  ALT=\"6x+-+2y+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since you know this equation is satisfied by x = 3 , y = -2 you substitute these values into<BR>\n" );
document.write( "the equation and both sides should be equal.  By substitution the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A3+-+2%2A%28-2%29+=+b ALIGN=MIDDLE  ALT=\"6%2A3+-+2%2A%28-2%29+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiplying out the terms on the left side results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18+%2B+4+=+b ALIGN=MIDDLE  ALT=\"18+%2B+4+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and adding the two terms on the left side tells you that b = 22.  That is the second <BR>\n" );
document.write( "quantity that you were supposed to find.<BR>\n" );
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document.write( "Hope this helps you to see your way through this word problem OK. </SPAN>\n" );
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