document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=127894>Question 127894</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am SO confused on this one, i already tried to solve this but when i checked by substittuting, they weren't equal.  \r<BR>\n" );
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document.write( "Solving Systems by Substitution:\r<BR>\n" );
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document.write( "a = 2/b - 3 <BR>\n" );
document.write( "a = 2b - 18\r<BR>\n" );
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document.write( "I'm supposed to find the solution as a point like: [2,-4]  but i have no idea if the a or b is x.  Please help me with this!  \r<BR>\n" );
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document.write( "I tried this: 2/b-3=2b-18 thats all i know that im pretty sure is right then times 2 on both sides -3=4b-18 then add 18  and -15=4b divide by 4 and thats 3.75 but when i put that into the other equation like 2*3.75 thats -10.5 and the final was -10.5 = 2/3.75 - 3  and thats -10.5 = .5 - 3 which is -10.5 does not equal -3.5  Im so confused and don't know what i did wrong!\r<BR>\n" );
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document.write( "THANK YOU SO MUCH </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #93800 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=93800\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solving Systems by Substitution:<BR>\n" );
document.write( "a = 2/b - 3<BR>\n" );
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document.write( "a = 2b - 18<BR>\n" );
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document.write( "I see you substituted (2/b - 3), from the 1st equation, for a in the 2nd equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Fb+-+3 ALIGN=MIDDLE  ALT=\"2%2Fb+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2b - 18 <BR>\n" );
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document.write( "get rid of the denominator by multiplying equation by b; (You multiplied by 2) then solve for b<BR>\n" );
document.write( "2 - 3b = 2b^2 - 18b<BR>\n" );
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document.write( "0 = 2b^2 - 18b + 3b - 2; arrange as a quadratic on the right<BR>\n" );
document.write( "OR<BR>\n" );
document.write( "2B^2 - 15B - 2 = 0; the normal way a quadratic equation is writte<BR>\n" );
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document.write( "This is a quadratic equation that has to be solved using the quadratic formula<BR>\n" );
document.write( "a = 2; b = -15; c = -2<BR>\n" );
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document.write( "The two solutions from that will be: b =-.131 and b = 7.631<BR>\n" );
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document.write( "Let's use b = 7.631 in the second equation to find a<BR>\n" );
document.write( "a = 2(7.631) - 18<BR>\n" );
document.write( "a = 14.262 - 18<BR>\n" );
document.write( "a = -2.738<BR>\n" );
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document.write( "So one pair of solutions will be a = -2.738, b = 7.631<BR>\n" );
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document.write( "We can assume a = y and b = x from the way the equations are written<BR>\n" );
document.write( "(the dependent variable is y and the left)\r<BR>\n" );
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document.write( "The x/y pair would be 7.631, -2.738<BR>\n" );
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document.write( "Check for equality in the 1st equation<BR>\n" );
document.write( "-2.738 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F7.631+-+3 ALIGN=MIDDLE  ALT=\"2%2F7.631+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-2.738 = .262 - 3<BR>\n" );
document.write( "-2.738 = -2.738; confirms this set of solutions<BR>\n" );
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document.write( "But the quadratic equation has another solution; b = -.131<BR>\n" );
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document.write( "Find a using this value for b in the 2nd equation<BR>\n" );
document.write( "a = 2(-.131) - 18<BR>\n" );
document.write( "a = -.262 - 18<BR>\n" );
document.write( "a = -18.262<BR>\n" );
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document.write( "Our other pair will be a = -18.262, b = -.131 (x/y -.131, -18.262)<BR>\n" );
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document.write( "Check to see if this will have equality in the 1st equation<BR>\n" );
document.write( "-18.262 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F-.131+-+3 ALIGN=MIDDLE  ALT=\"2%2F-.131+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-18.262 = -15.267 - 3<BR>\n" );
document.write( "-18.262 = -15.267; so this pair of solutions check out too<BR>\n" );
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document.write( "Did this help? I assume you know quadratic formula so I did not go thru that. </SPAN>\n" );
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