document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=598406>Question 598406</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help immediately :( <BR>\n" );
document.write( "I don't understand these equations , I was absent.<BR>\n" );
document.write( "I'm crying :(( I can't do all of these.<BR>\n" );
document.write( "[ Substitution ] \r<BR>\n" );
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document.write( "y=3x-4<BR>\n" );
document.write( "y= -5x + 4 \r<BR>\n" );
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document.write( "y=2x+13<BR>\n" );
document.write( "y=-4x-23\r<BR>\n" );
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document.write( "y=3x+20<BR>\n" );
document.write( "y=x+4\r<BR>\n" );
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document.write( "\n" );
document.write( "y=-4x-8<BR>\n" );
document.write( "y=3x+13\r<BR>\n" );
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document.write( "\n" );
document.write( "------\r<BR>\n" );
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document.write( "-x+y=6<BR>\n" );
document.write( "y=-7+14\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y=-5x+12<BR>\n" );
document.write( "x+y=-3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x+y=-6<BR>\n" );
document.write( "y=-3x-10\r<BR>\n" );
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document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-4x+5y=-15<BR>\n" );
document.write( "4x+y=21 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #378569 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=378569\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The basic idea is to replace one variable with another expression (of that other variable) so you can eliminate one variable.\r<BR>\n" );
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document.write( "This way, you'll have a single equation with one variable. You then solve that equation to find the value of that variable. Then you use the solution to find the value of the previously eliminated variable.\r<BR>\n" );
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document.write( "=======================================================\r<BR>\n" );
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document.write( "# 1\r<BR>\n" );
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document.write( "y=3x-4<BR>\n" );
document.write( "y= -5x + 4\r<BR>\n" );
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document.write( "y=3x-4\r<BR>\n" );
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document.write( "-5x+4=3x-4 ... Note: I'm replacing the 'y' with -5x+4 (since y = -5x+4)\r<BR>\n" );
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document.write( "-5x-3x=-4-4\r<BR>\n" );
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document.write( "-8x=-8\r<BR>\n" );
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document.write( "x=-8/(-8)\r<BR>\n" );
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document.write( "x = 1\r<BR>\n" );
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document.write( "-------------\r<BR>\n" );
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document.write( "y = 3x-4\r<BR>\n" );
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document.write( "y = 3(1)-4 ... Here I'm replacing 'x' with 1 (since x = 1)\r<BR>\n" );
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document.write( "y = 3-4\r<BR>\n" );
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document.write( "y = -1\r<BR>\n" );
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document.write( "So x = 1 and y = -1\r<BR>\n" );
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document.write( "=======================================================\r<BR>\n" );
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document.write( "# 2\r<BR>\n" );
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document.write( "y=2x+13<BR>\n" );
document.write( "y=-4x-23\r<BR>\n" );
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document.write( "y=2x+13\r<BR>\n" );
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document.write( "-4x-23=2x+13\r<BR>\n" );
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document.write( "-4x-2x=13+23\r<BR>\n" );
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document.write( "-6x=36\r<BR>\n" );
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document.write( "x=36/(-6)\r<BR>\n" );
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document.write( "x = -6\r<BR>\n" );
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document.write( "--------------\r<BR>\n" );
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document.write( "y = 2x+13\r<BR>\n" );
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document.write( "y = 2(-6)+13\r<BR>\n" );
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document.write( "y = -12+13\r<BR>\n" );
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document.write( "y = 1\r<BR>\n" );
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document.write( "So x = -6 and y = 1\r<BR>\n" );
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document.write( "=======================================================\r<BR>\n" );
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document.write( "# 3\r<BR>\n" );
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document.write( "y=3x+20<BR>\n" );
document.write( "y=x+4\r<BR>\n" );
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document.write( "y=3x+20\r<BR>\n" );
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document.write( "x+4=3x+20\r<BR>\n" );
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document.write( "x-3x=20-4\r<BR>\n" );
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document.write( "-2x=16\r<BR>\n" );
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document.write( "x=16/(-2)\r<BR>\n" );
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document.write( "x = -8\r<BR>\n" );
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document.write( "----------------\r<BR>\n" );
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document.write( "y = 3x+20\r<BR>\n" );
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document.write( "y = 3(-8)+20\r<BR>\n" );
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document.write( "y = -24+20\r<BR>\n" );
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document.write( "y = -4\r<BR>\n" );
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document.write( "So x = -8 and y = -4\r<BR>\n" );
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document.write( "=======================================================\r<BR>\n" );
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document.write( "# 4\r<BR>\n" );
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document.write( "y=-4x-8<BR>\n" );
document.write( "y=3x+13\r<BR>\n" );
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document.write( "y=-4x-8\r<BR>\n" );
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document.write( "3x+13=-4x-8\r<BR>\n" );
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document.write( "3x+4x=-8-13\r<BR>\n" );
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document.write( "7x=-21\r<BR>\n" );
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document.write( "x=-21/7\r<BR>\n" );
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document.write( "x=-3\r<BR>\n" );
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document.write( "-----------------\r<BR>\n" );
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document.write( "y = -4x-8\r<BR>\n" );
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document.write( "y = -4(-3)-8\r<BR>\n" );
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document.write( "y = 12-8\r<BR>\n" );
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document.write( "y = 4\r<BR>\n" );
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document.write( "So x = -3 and y = 4\r<BR>\n" );
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document.write( "=======================================================\r<BR>\n" );
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document.write( "# 5\r<BR>\n" );
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document.write( "-x+y=6<BR>\n" );
document.write( "y=-7+14\r<BR>\n" );
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document.write( "There's a typo in the second equation. Please repost this one. Thanks\r<BR>\n" );
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document.write( "=======================================================\r<BR>\n" );
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document.write( "# 6\r<BR>\n" );
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document.write( "y=-5x+12<BR>\n" );
document.write( "x+y=-3\r<BR>\n" );
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document.write( "\n" );
document.write( "x+y=-3\r<BR>\n" );
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document.write( "x+(-5x+12)=-3\r<BR>\n" );
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document.write( "x-5x+12=-3\r<BR>\n" );
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document.write( "x-5x=-3-12\r<BR>\n" );
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document.write( "-4x=-15\r<BR>\n" );
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document.write( "x=-15/(-4)\r<BR>\n" );
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document.write( "x=15/4\r<BR>\n" );
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document.write( "----------------\r<BR>\n" );
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document.write( "y = -5x+12\r<BR>\n" );
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document.write( "y = -5(15/4)+12\r<BR>\n" );
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document.write( "y = -75/4+12\r<BR>\n" );
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document.write( "y = -75/4+48/4\r<BR>\n" );
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document.write( "y = -27/4\r<BR>\n" );
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document.write( "So x = 15/4 and y = -27/4\r<BR>\n" );
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document.write( "=======================================================\r<BR>\n" );
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document.write( "# 7\r<BR>\n" );
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document.write( "x+y=-6<BR>\n" );
document.write( "y=-3x-10\r<BR>\n" );
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document.write( "x+y=-6\r<BR>\n" );
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document.write( "x+(-3x-10)=-6\r<BR>\n" );
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document.write( "x-3x-10=-6\r<BR>\n" );
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document.write( "x-3x=-6+10\r<BR>\n" );
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document.write( "-2x=4\r<BR>\n" );
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document.write( "x=4/(-2)\r<BR>\n" );
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document.write( "x = -2\r<BR>\n" );
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document.write( "------------------\r<BR>\n" );
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document.write( "y = -3x-10\r<BR>\n" );
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document.write( "y = -3(-2)-10\r<BR>\n" );
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document.write( "y = 6-10\r<BR>\n" );
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document.write( "y = -4\r<BR>\n" );
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document.write( "So x = -2 and y = -4\r<BR>\n" );
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document.write( "=======================================================\r<BR>\n" );
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document.write( "# 8\r<BR>\n" );
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document.write( "-4x+5y=-15<BR>\n" );
document.write( "4x+y=21\r<BR>\n" );
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document.write( "First we need to solve one equation for one variable. I'm going to solve the second equation for y.\r<BR>\n" );
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document.write( "4x+y=21\r<BR>\n" );
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document.write( "y=21-4x\r<BR>\n" );
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document.write( "y = -4x+21\r<BR>\n" );
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document.write( "-----------\r<BR>\n" );
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document.write( "Now use substitution to solve\r<BR>\n" );
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document.write( "-4x+5y=-15\r<BR>\n" );
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document.write( "-4x+5(-4x+21)=-15\r<BR>\n" );
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document.write( "-4x-20x+105=-15\r<BR>\n" );
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document.write( "-4x-20x=-15-105\r<BR>\n" );
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document.write( "-24x=-120\r<BR>\n" );
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document.write( "x=-120/(-24)\r<BR>\n" );
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document.write( "x = 5\r<BR>\n" );
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document.write( "-----------\r<BR>\n" );
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document.write( "y = -4x+21\r<BR>\n" );
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document.write( "y = -4(5)+21\r<BR>\n" );
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document.write( "y = -20+21\r<BR>\n" );
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document.write( "y = 1\r<BR>\n" );
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document.write( "So x = 5 and y = 1 </SPAN>\n" );
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