document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=845824>Question 845824</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Need help solving ASAP! Use the substitution method to solve the system of equations. <BR>\n" );
document.write( "4(x - 2) = 8(y - 1)<BR>\n" );
document.write( "16y - 32 = 2x + 4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #509468 by </B><A HREF=/tutors/aboutme.mpl?userid=pmesler><B>pmesler(52)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=pmesler><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=pmesler><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=509468\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This one was fun. The key to solving this is to simplify first. Let's start off by labeling the different equations as equations 1 and 2\r<BR>\n" );
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document.write( "1) 4(x - 2) = 8(y - 1)<BR>\n" );
document.write( "2) 16y - 32 = 2x + 4\r<BR>\n" );
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document.write( "The first thing you want to do is simplify equation 1 by using the distributive property to simplify both sides of the equation.\r<BR>\n" );
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document.write( "So equation 1 looks like this after using the distributive property:\r<BR>\n" );
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document.write( "4x-8 = 8y-8 \r<BR>\n" );
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document.write( "Now, once we have this simplified we want to simplify it even more. Let's try to get the y alone. We do that by dividing both sides by 8 to get this:\r<BR>\n" );
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document.write( "1/2x-8 = y-8 \r<BR>\n" );
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document.write( "Now we just add 8 to both sides to get y by itself and we get this:\r<BR>\n" );
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document.write( "y = 1/2x. \r<BR>\n" );
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document.write( "So now we can express y in terms of x. Now let's use that knowledge to solve for equation 2\r<BR>\n" );
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document.write( "Equation 2 says <BR>\n" );
document.write( "16y - 32 = 2x + 4.\r<BR>\n" );
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document.write( "Now all you need to do is substitute what we know y is into the equation and solve for x since we can now express y in terms of x.\r<BR>\n" );
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document.write( "16(1/2x) - 32 = 2x + 4. Now, solve for x.\r<BR>\n" );
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document.write( "Equation 2 becomes \r<BR>\n" );
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document.write( "8x - 32 = 2x + 4.\r<BR>\n" );
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document.write( "Subtract 2x from both sides\r<BR>\n" );
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document.write( "6x - 32 = 4 \r<BR>\n" );
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document.write( "Add 32 to both sides.\r<BR>\n" );
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document.write( "6x = 36\r<BR>\n" );
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document.write( "Divide each side by 6.\r<BR>\n" );
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document.write( "x = 6\r<BR>\n" );
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document.write( "And since we know that y =1/2x that means y = 3. \r<BR>\n" );
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document.write( "Now plug in the values of x and y into the original equations to see of they check out.\r<BR>\n" );
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document.write( "4(6-2) = 8(3-1)\r<BR>\n" );
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document.write( "4(4) = 8(2)\r<BR>\n" );
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document.write( "16 = 16. Everything checks out for equation 1 so let's try equation 2\r<BR>\n" );
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document.write( "16(3)-32 = 2(6) + 4\r<BR>\n" );
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document.write( "48 - 32 = 12 + 4\r<BR>\n" );
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document.write( "16 = 16. Equation 2 checks out so the solution is (6,3). \r<BR>\n" );
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document.write( " </SPAN>\n" );
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