document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148873>Question 148873</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4-(y-3) = x+3 1st equation<BR>\n" );
document.write( "10+x<BR>\n" );
document.write( "&#8213;—&#8213;— = 2+(y-12) 2nd equation<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109259 by </B><A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><B>Electrified_Levi(103)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><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=109259\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, Hope I can help,<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4-%28y-3%29+=+x%2B3+ ALIGN=MIDDLE  ALT=\"+4-%28y-3%29+=+x%2B3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (1st equation)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2810%2Bx%29%2F3+=+2%2B%28y-12%29+ ALIGN=MIDDLE  ALT=\"+%2810%2Bx%29%2F3+=+2%2B%28y-12%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (2nd equation)<BR>\n" );
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document.write( "If you are trying to solve for \"x\" and \"y\", this is how you do it.<BR>\n" );
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document.write( "First, you have to reduce each equation to (Ax+By=C) form, we will do the first equation.<BR>\n" );
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document.write( "We will take the parentheses off<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4+-+y+%2B+3+=+x+%2B+3+ ALIGN=MIDDLE  ALT=\"+4+-+y+%2B+3+=+x+%2B+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We will add on the left side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4+%2B+3+-+y+=+x+%2B+3+ ALIGN=MIDDLE  ALT=\"+4+%2B+3+-+y+=+x+%2B+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7+-+y+=+x+%2B+3+ ALIGN=MIDDLE  ALT=\"+7+-+y+=+x+%2B+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We will move the \"y\" to the right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7+=+x+%2B+y+%2B+3+ ALIGN=MIDDLE  ALT=\"+7+=+x+%2B+y+%2B+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We will now move the \"3\" to the left side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4+=+x+%2B+y+ ALIGN=MIDDLE  ALT=\"+4+=+x+%2B+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Our first equation is (x + y = 4)<BR>\n" );
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document.write( "Now we will solve the second equation<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2810%2Bx%29%2F3+=+2%2B%28y-12%29+ ALIGN=MIDDLE  ALT=\"+%2810%2Bx%29%2F3+=+2%2B%28y-12%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We can multiply everything by \"3\" to get rid of the fraction<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%2810%2Bx%29%2F3%29%283%29+=+2%283%29%2B%28y-12%29%283%29+ ALIGN=MIDDLE  ALT=\"+%28%2810%2Bx%29%2F3%29%283%29+=+2%283%29%2B%28y-12%29%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "It will get rid of the denominator of the fraction<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10%2Bx+=+6+%2B+3%28y-12%29+ ALIGN=MIDDLE  ALT=\"+10%2Bx+=+6+%2B+3%28y-12%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We will get rid of the parentheses on the right side, using distribution method<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10%2Bx+=+6+%2B+3y+-+36+ ALIGN=MIDDLE  ALT=\"+10%2Bx+=+6+%2B+3y+-+36+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We will subtract the right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10%2Bx+=+%28-30%29+%2B+3y++ ALIGN=MIDDLE  ALT=\"+10%2Bx+=+%28-30%29+%2B+3y++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We will move \"3y\" to the left side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10+%2B+x+-+3y+=+%28-30%29+ ALIGN=MIDDLE  ALT=\"+10+%2B+x+-+3y+=+%28-30%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We will move \"10\" to the right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+-+3y+=+%28-40%29+ ALIGN=MIDDLE  ALT=\"+x+-+3y+=+%28-40%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Our reduced second equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+-+3y+=+%28-40%29+ ALIGN=MIDDLE  ALT=\"+x+-+3y+=+%28-40%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We can now put the two equations side by side and solve for \"x\" and \"y\"<BR>\n" );
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document.write( "x + y = 4<BR>\n" );
document.write( "x - 3y = (-40)<BR>\n" );
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document.write( "I will show you two different ways to solve these problems, one is a method that can be done on certain problems, the other you can do on any problem.<BR>\n" );
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document.write( "(First Method) If you can either add or subtract the equations to get rid of a letter, this method works, we can subtract the equations to get rid of \"x\"<BR>\n" );
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document.write( "x + y = 4<BR>\n" );
document.write( "- (x - 3y = (-40))<BR>\n" );
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document.write( "Getting rid of parentheses<BR>\n" );
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document.write( "x + y = 4<BR>\n" );
document.write( "-x + 3y = +40<BR>\n" );
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document.write( "It will become<BR>\n" );
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document.write( "0x + 4y = 44<BR>\n" );
document.write( "4y = 44<BR>\n" );
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document.write( "We can divide everything by \"4\" to get \"y\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4y%2F4+=+44%2F4+ ALIGN=MIDDLE  ALT=\"+4y%2F4+=+44%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+11+ ALIGN=MIDDLE  ALT=\"+y+=+11+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We can now replace \"y\" with \"11\" in one of our equations<BR>\n" );
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document.write( "x + y = 4<BR>\n" );
document.write( "x + (11) = 4<BR>\n" );
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document.write( "We can move \"11\" to the right side<BR>\n" );
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document.write( "x + 11 - 11 = 4 - 11<BR>\n" );
document.write( "x = (-7)<BR>\n" );
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document.write( "We can check by replacing \"x\" and \"y\" in our second equation<BR>\n" );
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document.write( "x - 3y = (-40)<BR>\n" );
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document.write( "(-7) - 3(11) = (-40)<BR>\n" );
document.write( "(-40)=(-40)<BR>\n" );
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document.write( "The solution set is (x,y), our solution set is (-7,11)<BR>\n" );
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document.write( "(Second Method) This method works on any problem like this, <BR>\n" );
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document.write( "First, we solve for a letter(doesn't matter which one, usually the easiest one) in both of the equations, we will use \"x\"<BR>\n" );
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document.write( "(First Equation) x + y = 4<BR>\n" );
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document.write( "We will move the \"y\" to the right side<BR>\n" );
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document.write( "x + y - y = 4 - y<BR>\n" );
document.write( "(x = 4 - y), or (x = (-y) + 4)<BR>\n" );
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document.write( "((-y) + 4) is our first answer<BR>\n" );
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document.write( "We will now solve \"x\" in our second equation<BR>\n" );
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document.write( "x - 3y = (-40)<BR>\n" );
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document.write( "We will move (-3y) to the right side<BR>\n" );
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document.write( "x - 3y + 3y = (-40) + 3y<BR>\n" );
document.write( "(x = (-40) + 3y), or (x = 3y - 40)<BR>\n" );
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document.write( "(3y - 40) is our second answer<BR>\n" );
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document.write( "We can put the two answers together, since they equal each other<BR>\n" );
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document.write( "((-y) + 4) = (3y - 40)<BR>\n" );
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document.write( "We will get rid of the first sets of parentheses<BR>\n" );
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document.write( "(-y) + 4 = 3y - 40<BR>\n" );
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document.write( "We will move (-y) to the right side<BR>\n" );
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document.write( "(-y) + y + 4 = 3y + y - 40<BR>\n" );
document.write( "4 = 4y - 40<BR>\n" );
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document.write( "We will move (-40) to the left side<BR>\n" );
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document.write( "4 + 40 = 4y - 40 + 40<BR>\n" );
document.write( "44 = 4y<BR>\n" );
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document.write( "We can divide everything by 4<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+44%2F4+=+4y%2F4+ ALIGN=MIDDLE  ALT=\"+44%2F4+=+4y%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "11 = y<BR>\n" );
document.write( "y = 11<BR>\n" );
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document.write( "We will now replace \"y\" with \"11\" in our second equation(we will solve \"x\" a different way this time)<BR>\n" );
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document.write( "x - 3y = (-40)<BR>\n" );
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document.write( "x - 3(11) = (-40)<BR>\n" );
document.write( "x - 33 = (-40)<BR>\n" );
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document.write( "We will move (-33) to the right side<BR>\n" );
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document.write( "x - 33 + 33 = (-40) + 33<BR>\n" );
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document.write( "x = (-7)<BR>\n" );
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document.write( "We can replace \"x\" and \"y\" in our first equation, to check our answers<BR>\n" );
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document.write( "x + y = 4<BR>\n" );
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document.write( "(-7) + (11) = 4<BR>\n" );
document.write( "4 = 4<BR>\n" );
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document.write( "Our answers are<BR>\n" );
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document.write( "x = (-7)<BR>\n" );
document.write( "y = (11)<BR>\n" );
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document.write( "Our solution set is (-7,11)<BR>\n" );
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document.write( "Hope I helped, Levi </SPAN>\n" );
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