document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118133>Question 118133</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the values for m and b in the following system so that the solution to the system is (-3,4). 5x + 7y =b and mx + y =22. First; 5x+7y=b, =>5(-3)+7(4)=b,<BR>\n" );
document.write( "=>-15+28=b, =>13=b. Now this one; mx + y=22; =>m(-3)+4=22, =>-3m=22-4=18, <BR>\n" );
document.write( "=>-3m=18, =>m=18/(-3), =>m=-6. So then b=13 and m=-6.<BR>\n" );
document.write( "I just want to know if I am correct please?\r<BR>\n" );
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document.write( "Thank you, Barb Neely<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86242 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=86242\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are correct.<BR>\n" );
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document.write( "A way you could convince yourself is to start with the equation set that you derived after<BR>\n" );
document.write( "doing your work:<BR>\n" );
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document.write( "+5x + 7y = 13 and<BR>\n" );
document.write( "-6x + y = 22<BR>\n" );
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document.write( "You could solve them simultaneously and see if the answers for x and y are (-3,4)<BR>\n" );
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document.write( "For example ... multiply the bottom equation (both sides, all terms) by -7 to make the equation<BR>\n" );
document.write( "set become:<BR>\n" );
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document.write( "+5x + 7y = 13  <BR>\n" );
document.write( "42x - 7y = -154<BR>\n" );
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document.write( "Add these two equations together in vertical columns to make the terms containing y<BR>\n" );
document.write( "cancel each other out and you end up with the \"combined\" equation of:<BR>\n" );
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document.write( "47x = -141<BR>\n" );
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document.write( "Solve for x by dividing both sides by 47 and you get that x = -3.<BR>\n" );
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document.write( "Next go back to one of the equations you developed and substitute -3 for x. If you do, you<BR>\n" );
document.write( "find that y = +4. This being the case you can say that (-3, 4) is the common solution, just<BR>\n" );
document.write( "as it should be ...<BR>\n" );
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document.write( "Or you could go to each of your derived equations one at a time ... and substitute -3 <BR>\n" );
document.write( "for x and +4 for y to see if each equation balances (left side equals right side) after<BR>\n" );
document.write( "those substitutions. Both equations should balance ... as you might expect because you<BR>\n" );
document.write( "are basically just following the process that you originally did to solve for b and m.<BR>\n" );
document.write( "If both don't balance, then you would have to check your original work to find the error.<BR>\n" );
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document.write( "Good job of seeing your way through this problem ....<BR>\n" );
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