document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=335143>Question 335143</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In an substitution problem, when you have two variables on one side of the equal sign, what do I do? <BR>\n" );
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document.write( "3x - y = 5<BR>\n" );
document.write( "-4x + 2y = -6\r<BR>\n" );
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document.write( "I know it is dependent, but I don't know how to get there! I did the other day... but now can't remember and have my final tomorrow.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #240189 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=240189\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have 2 equations in 2 unknowns.\r<BR>\n" );
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document.write( "You want to substitute for one of the variables to get one equation in one unknown.\r<BR>\n" );
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document.write( "At least that's what I think you're asking.\r<BR>\n" );
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document.write( "Take the first equation and solve for x or y.  \r<BR>\n" );
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document.write( "We'll do y.\r<BR>\n" );
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document.write( "You start with 3x - y = 5\r<BR>\n" );
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document.write( "Add y to both sides of this equation and subtract 5 from both sides of this equation to get:\r<BR>\n" );
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document.write( "y = 3x - 5\r<BR>\n" );
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document.write( "Substitute for y in the second equation.\r<BR>\n" );
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document.write( "The second equation is -4x + 2y = -6\r<BR>\n" );
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document.write( "Substitute for y in the second equation by the value of y that you solved for in the first equation to get:\r<BR>\n" );
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document.write( "-4x + 2 * (3x-5) = -6\r<BR>\n" );
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document.write( "Simplify this by multiplying out the factors to get:\r<BR>\n" );
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document.write( "-4x + 6x - 10 = -6\r<BR>\n" );
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document.write( "Add 10 to both sides of this equation and combine like terms to get:\r<BR>\n" );
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document.write( "2x = 4\r<BR>\n" );
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document.write( "Divide both sides of this equation by 2 to get:\r<BR>\n" );
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document.write( "x = 2\r<BR>\n" );
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document.write( "Now that you know the value of x, you can solve for  y in either of the original 2 equations.\r<BR>\n" );
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document.write( "From the first equation,  you have 3x - y = 5\r<BR>\n" );
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document.write( "Substitute for x in this equation to get:\r<BR>\n" );
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document.write( "3*2 - y = 5 which becomes:\r<BR>\n" );
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document.write( "6 - y = 5\r<BR>\n" );
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document.write( "Subtract 6 from both sides of this equation to get:\r<BR>\n" );
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document.write( "-y = -1\r<BR>\n" );
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document.write( "Multiply both sides of this equation by -1 to get:\r<BR>\n" );
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document.write( "y = 1\r<BR>\n" );
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document.write( "You now have:\r<BR>\n" );
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document.write( "x = 2 and y = 1\r<BR>\n" );
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document.write( "Substitute in both original equations to see if they are true.\r<BR>\n" );
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document.write( "3x - y = 5 becomes 3*2 - 1 = 5 which becomes 6 - 1 = 5 which becomes 5 = 5 which is true.\r<BR>\n" );
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document.write( "-4x + 2y = -6 becomes -4*2 + 2*1 = -6 which becomes -8 + 2 = -6 which becomes -6 = -6 which is true.\r<BR>\n" );
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document.write( "Both original equations are true, so the values of x = 2 and y = 1 are good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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