document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171788>Question 1171788</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of 3 numbers is 21. 3 times the first number increased by four times the second number plus the third number is 14. The sum of two times the first and seven times the second number, increased by the third number is -18. If the first number is represented by x, the second number is represented by y, and the third number is represented by a, write a system of equation that could be used to solve for the variables.\r<BR>\n" );
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document.write( "Can someone give me step by step instructions on how to solve problems like this? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #796725 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=796725\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sum of 3 numbers is 21. 3 times the first number increased by four times the second number plus the third number is 14. The sum of two times the first and seven times the second number, increased by the third number is -18. If the first number is represented by x, the second number is represented by y, and the third number is represented by a, write a system of equation that could be used to solve for the variables.<BR>\n" );
document.write( "Can someone give me step by step instructions on how to solve problems like this?<BR>\n" );
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document.write( "Write an equation for each statement<BR>\n" );
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document.write( " The sum of 3 numbers is 21.<BR>\n" );
document.write( "x + y + a = 21<BR>\n" );
document.write( " 3 times the first number increased by four times the second number plus the third number is 14.<BR>\n" );
document.write( "3x + 4y + a = 14<BR>\n" );
document.write( " The sum of two times the first and seven times the second number, increased by the third number is -18.<BR>\n" );
document.write( "2x + 7y + a = -18<BR>\n" );
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document.write( "Use elimination on the 1st two equation<BR>\n" );
document.write( "3x + 4y + a = 14<BR>\n" );
document.write( " x +  y + a = 21<BR>\n" );
document.write( "------------------Subtraction eliminates a<BR>\n" );
document.write( "2x + 3y = -7<BR>\n" );
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document.write( "Do the same on the 1st and 3rd equation<BR>\n" );
document.write( "2x + 7y + a = -18<BR>\n" );
document.write( " x + y  + a = 21<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "x + 6y = -39<BR>\n" );
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document.write( "Take the resulting equations, multiply the above by 2<BR>\n" );
document.write( "2x + 12y = -78<BR>\n" );
document.write( "2x + 3y  = -7<BR>\n" );
document.write( "----------------Subtraction eliminates x, find y<BR>\n" );
document.write( "9y = -71<BR>\n" );
document.write( "y = -71/9<BR>\n" );
document.write( "y = -7.8888<BR>\n" );
document.write( "At this point it is apparent that the solutions are not integers. which leads me to suspect there is a mistake in the problem.<BR>\n" );
document.write( "Anyway, find x<BR>\n" );
document.write( "x + 6(-7.888) = -39<BR>\n" );
document.write( "x + -47.333 = - 39<BR>\n" );
document.write( "x = -39 + 47.3333<BR>\n" );
document.write( "x = 8.3333<BR>\n" );
document.write( "Find a<BR>\n" );
document.write( "8.333 - 7.888 + a = 21<BR>\n" );
document.write( ".445 + a = 21<BR>\n" );
document.write( "a = 21 -.445<BR>\n" );
document.write( "a = 20.555<BR>\n" );
document.write( "I confirmed these solutions using the matrix feature on my Calc\r<BR>\n" );
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document.write( " </SPAN>\n" );
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