document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=27858>Question 27858</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4x+2y=14<BR>\n" );
document.write( "7x-3y=-8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #15172 by </B><A HREF=/tutors/aboutme.mpl?userid=Sridi><B>Sridi(6)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Sridi><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=15172\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We need to eliminate one of the variables first to solve the system of equations. <BR>\n" );
document.write( "either we can eliminate the x variable, solve for y first or the other way around.\r<BR>\n" );
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document.write( "Let us call <BR>\n" );
document.write( "4x+2y=14 --------Equation 1<BR>\n" );
document.write( "7x-3y=-8 -------- Equation 2\r<BR>\n" );
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document.write( "Now multiply the entire equation 1 by 3 and equation 2 by 2\r<BR>\n" );
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document.write( "(4x+2y=14) * 3<BR>\n" );
document.write( "(7x-3y=-8) * 2\r<BR>\n" );
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document.write( "we will get\r<BR>\n" );
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document.write( "12x + 6y = 42    -------Equation 1a<BR>\n" );
document.write( "14x -6y = - 16  ------- Equation 2b\r<BR>\n" );
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document.write( "Now add equation 1a and 2b\r<BR>\n" );
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document.write( "The =6y will cancel with -6y\r<BR>\n" );
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document.write( "You are left with<BR>\n" );
document.write( "26x = 26\r<BR>\n" );
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document.write( "X = 26/26\r<BR>\n" );
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document.write( "X = 1\r<BR>\n" );
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document.write( "Now substitute x = 1 in equation 1\r<BR>\n" );
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document.write( "4(1) + 2y = 14\r<BR>\n" );
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document.write( "2y+4 + 14\r<BR>\n" );
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document.write( "2y = 14- 4 = 10\r<BR>\n" );
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document.write( "2y = 10\r<BR>\n" );
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document.write( "y = 5\r<BR>\n" );
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document.write( "Now check with equation 2 with x = 1 and y = 5\r<BR>\n" );
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document.write( "7(1) - 3(5) = 7 - 15 = -8.\r<BR>\n" );
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document.write( "We have proved that 7x - 3y = -8 just like equation 2 is with the values we calculated for x and y. hence x =1, and y = 5 are correct answers for the sytem of equation given.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );