document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=16303>Question 16303</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the variables<BR>\n" );
document.write( "3x+4y-3c=5<BR>\n" );
document.write( "x+6y+2c=3<BR>\n" );
document.write( "6x+2y+3c=4<BR>\n" );
document.write( "Please help me out this with step by step solution<BR>\n" );
document.write( "thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #7941 by </B><A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><B>AnlytcPhil(1806)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><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=AnlytcPhil><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=7941\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face = \"courier new\"<BR>\n" );
document.write( "find the variables<BR>\n" );
document.write( "3x+4y-3c=5<BR>\n" );
document.write( "x+6y+2c=3<BR>\n" );
document.write( "6x+2y+3c=4<BR>\n" );
document.write( "`<BR>\n" );
document.write( "1. Does any of the three equations contain only two letters?<BR>\n" );
document.write( "2. If the answer to 1 is yes, choose that letter to eliminate first.<BR>\n" );
document.write( "3. If the answer to 1 is no, choose any of the three letters to eliminate first.<BR>\n" );
document.write( "4. Choose a pair of equations that contains the letter to eliminate first.<BR>\n" );
document.write( "5. Eliminate that letter from the pair of equations chosen in 4.<BR>\n" );
document.write( "6. If the answer to 1 was yes, solve the system of two equations and one<BR>\n" );
document.write( "unknown consisting of the original equation that contained only two letters and<BR>\n" );
document.write( "the resulting equation from 5 for those two letters.<BR>\n" );
document.write( "7. If the answer to 1 was no, choose a different pair of equations from the pair chosen in 4, and eliminate the letter chosen in step 3.<BR>\n" );
document.write( "8. If the answer to 1 was no, solve the system of two equations and two<BR>\n" );
document.write( "unknowns from steps 5 and 7<BR>\n" );
document.write( "9. Choose any one of the original equations that contains the letter that was<BR>\n" );
document.write( "eliminated first.<BR>\n" );
document.write( "10. Substitute the values of the two variables found in step 6 or step 7<BR>\n" );
document.write( "11. Solve for the variable eliminated first.<BR>\n" );
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document.write( "3x+4y-3c=5<BR>\n" );
document.write( "x+6y+2c=3<BR>\n" );
document.write( "6x+2y+3c=4<BR>\n" );
document.write( "`<BR>\n" );
document.write( "`<BR>\n" );
document.write( "1. Does any of the three equations contain only two letters?<BR>\n" );
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document.write( "The answer is no. So go on to step 2<BR>\n" );
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document.write( "2. If the answer to 1 is yes, choose that letter to eliminate first.<BR>\n" );
document.write( "`<BR>\n" );
document.write( "The answer to 1 was no, so go on to step 3<BR>\n" );
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document.write( "3. If the answer to 1 is no, choose any of the three letters to eliminate first.<BR>\n" );
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document.write( "Choose c.<BR>\n" );
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document.write( "4. Choose a pair of equations that contains the letter to eliminate first.<BR>\n" );
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document.write( "Choose 1 and 3.<BR>\n" );
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document.write( "5. Eliminate that letter from the pair of equations chosen in 4.<BR>\n" );
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document.write( "3x + 4y - 3c = 5<BR>\n" );
document.write( "6x + 2y + 3c = 4<BR>\n" );
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document.write( "Add these two vertically term by term and the c terms cancel<BR>\n" );
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document.write( "9x + 6y = 9<BR>\n" );
document.write( "`<BR>\n" );
document.write( "6. If the answer to 1 was yes, solve the system of two equations and one<BR>\n" );
document.write( "unknown consisting of the original equation that contained only two letters<BR>\n" );
document.write( "and the resulting equation from 5 for those two letters.<BR>\n" );
document.write( "`<BR>\n" );
document.write( "The answer to 1 was no, so go on to step 7<BR>\n" );
document.write( "`<BR>\n" );
document.write( "7. If the answer to 1 was no, choose a different pair of equations from the<BR>\n" );
document.write( "pair chosen in 4, and do step 5.<BR>\n" );
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document.write( "Choose the first and second equations:<BR>\n" );
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document.write( "3x + 4y - 3c = 5<BR>\n" );
document.write( "`x + 6y + 2c = 3<BR>\n" );
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document.write( "We must eliminate c.  Multiply the first equation through by 2, and the second<BR>\n" );
document.write( "equation through by 3 and add vertically term by term:<BR>\n" );
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document.write( "6x +  8y - 6c = 10<BR>\n" );
document.write( "3x + 18y + 6c =` 9<BR>\n" );
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document.write( "9x + 26y ` ` `= 19<BR>\n" );
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document.write( "8. If the answer to 1 was no, solve the system of two equations and two unknowns from steps 5 and 7.<BR>\n" );
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document.write( "9x +` 6y =` 9<BR>\n" );
document.write( "9x + 26y = 19<BR>\n" );
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document.write( "Multiply the first equation by -1 and add them vertically term by term:<BR>\n" );
document.write( "`<BR>\n" );
document.write( "-9x - `6x = -9<BR>\n" );
document.write( "`9x + 26y = 19<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "` ` ` 20y = 10<BR>\n" );
document.write( "` ` ` ` y = 1/2<BR>\n" );
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document.write( "Substitute 1/2 for y in the first equation 9x + 6y = 9<BR>\n" );
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document.write( "9x + 6(1/2) = 9<BR>\n" );
document.write( "9x + 3 = 9<BR>\n" );
document.write( "9x = 6<BR>\n" );
document.write( "`x = 6/9 = 2/3<BR>\n" );
document.write( "`<BR>\n" );
document.write( "9. Choose any one of the original equations that contains the letter that was<BR>\n" );
document.write( "eliminated first.<BR>\n" );
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document.write( "Choose the second original equation, x + 6y + 2c = 3<BR>\n" );
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document.write( "10. Substitute the values of the two variables found in step 6 or step 7<BR>\n" );
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document.write( "We substitute 2/3 for x and 1/2 for y<BR>\n" );
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document.write( "x + 6y + 2c = 3<BR>\n" );
document.write( "(2/3) + 6(1/2) + 2c = 3<BR>\n" );
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document.write( "11. Solve for the variable eliminated first<BR>\n" );
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document.write( "2/3 + 3 + 2c = 3<BR>\n" );
document.write( "` ` ` ` ` 2c = -2/3<BR>\n" );
document.write( "` ` ` ` ` `c = -1/3<BR>\n" );
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document.write( "Edwin<BR>\n" );
document.write( "AnlytcPhil@aol.com\r<BR>\n" );
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document.write( "    <BR>\n" );
document.write( " </SPAN>\n" );
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