document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=70698>Question 70698</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the best method to solve each system of equations. Then solve the system. \r<BR>\n" );
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document.write( "2x+y=3x-15<BR>\n" );
document.write( "x+5=4y+2x\r<BR>\n" );
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document.write( "I have (18 1/3, -3 1/2)\r<BR>\n" );
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document.write( "Is this correct. Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #50493 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=50493\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your answer is incorrect.  Maybe I can help you to find your error. Let's begin by simplifying <BR>\n" );
document.write( "the two equations a little.<BR>\n" );
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document.write( "The first equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+y+=+3x+-+15 ALIGN=MIDDLE  ALT=\"2x+%2B+y+=+3x+-+15\"   DISABLED_style= \"max-width:90%; height:auto;\" >. You have two terms that contain x.  Let's move<BR>\n" );
document.write( "the x from the right side by adding -3x to it.  This cancels the +3x on the right side.  However,<BR>\n" );
document.write( "if you add -3x to the right side, you must also add -3x to the left side.  When you do that<BR>\n" );
document.write( "you add the -3x to the +2x that is already on the left side.  The result is -x.  So the first<BR>\n" );
document.write( "equation is reduced to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+%2B+y+=+-15 ALIGN=MIDDLE  ALT=\"-x+%2B+y+=+-15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That's a little easier to work with.  Now let's go to work on the second equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5=4y%2B2x ALIGN=MIDDLE  ALT=\"x%2B5=4y%2B2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice the right side has only terms with variables. Let's move them to the left side so<BR>\n" );
document.write( "the equation has all the terms containing x and y on the left side just like the first<BR>\n" );
document.write( "equation does. Let's first add -2x to both sides.  On the right side the -2x cancels<BR>\n" );
document.write( "the +2x so the +2x disappears. And on the left side you add the -2x to the +x to get the<BR>\n" );
document.write( "sum of -x.  Now add -4y to the right side term of +4x.  When you do the 4x is canceled and<BR>\n" );
document.write( "you are left with zero on the right side. There is no y term on the left side so when we<BR>\n" );
document.write( "add -4y that term appears on the left side unchanged. At this point the second equation is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+-+4y+%2B+5+=+0 ALIGN=MIDDLE  ALT=\"-x+-+4y+%2B+5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice now that the +5 should be on the right side instead of the left side.  Move this<BR>\n" );
document.write( "term to the right side by adding -5 to both sides.  The -5 adds to the +5 on the left side<BR>\n" );
document.write( "and it cancels it out.  On the right side when we add -5 to 0 the result is -5. So finally <BR>\n" );
document.write( "we are at the point of knowing that the second equation is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+-+4y+=+-5 ALIGN=MIDDLE  ALT=\"-x+-+4y+=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now we are at the point of saying that our set of two equations has been changed to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+%2B+y+=+-15 ALIGN=MIDDLE  ALT=\"-x+%2B+y+=+-15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+-+4y+=+-5 ALIGN=MIDDLE  ALT=\"-x+-+4y+=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "To eliminate the x term we can subtract the second equation from the first equation. <BR>\n" );
document.write( "(If you prefer you can think of multiplying the entire second equation by -1 and then adding <BR>\n" );
document.write( "it to the first equation.) As a result of this subtraction, the x terms disappear.<BR>\n" );
document.write( "The y term of the answer is 5y and the numbers on the right side subtract to give an<BR>\n" );
document.write( "answer of -10.  We are left with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y+=+-10 ALIGN=MIDDLE  ALT=\"5y+=+-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "which we can solve by dividing both sides by 5 to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-2 ALIGN=MIDDLE  ALT=\"y+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now knowing that y = -2, we can return to either of the original equations and substitute<BR>\n" );
document.write( "-2 for y. Then we can solve for x.  Let's return to the original first equation of:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+y+=+3x+-+15 ALIGN=MIDDLE  ALT=\"2x+%2B+y+=+3x+-+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "When we substitute -2 for y in this equation, the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+-+2+=+3x+-+15 ALIGN=MIDDLE  ALT=\"2x+-+2+=+3x+-+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then we can add +2 to both sides. Following that we add -3x to both sides. Do you see why?<BR>\n" );
document.write( "The resulting equation is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+=+-13 ALIGN=MIDDLE  ALT=\"-x+=+-13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since we are to solve for +x, we can do so by multiplying both sides by -1 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+13 ALIGN=MIDDLE  ALT=\"x+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In summary the answers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=13 ALIGN=MIDDLE  ALT=\"x=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2 ALIGN=MIDDLE  ALT=\"y=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hopefully this will help you to understand the problem and to track down your errors.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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