document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=462114>Question 462114</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How to solve systems of linear equations such as this one.<BR>\n" );
document.write( "4x - y = -4<BR>\n" );
document.write( "12 - 3y = 24 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #316839 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=316839\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How to solve systems of linear equations such as this one.<BR>\n" );
document.write( "4x - y = -4<BR>\n" );
document.write( "12 - 3y = 24<BR>\n" );
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document.write( "I wonder if you meant 12x - 3y = 24 rather than 12 - 3y = 24.<BR>\n" );
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document.write( "I will solve the problem you typed in. If you need more help, post a new question, or send me a message.<BR>\n" );
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document.write( "You have two linear equations here. On a coordinate graph, the are two straight lines which intersect a single point (x, y). We will use algebra to find the coordinates of the intersection point.<BR>\n" );
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document.write( "First, let's simplify the second equation:<BR>\n" );
document.write( "12 - 3y = 24<BR>\n" );
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document.write( "Subtract 12 from both sides.<BR>\n" );
document.write( "-3y = 24 - 12<BR>\n" );
document.write( "-3y = 12<BR>\n" );
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document.write( "Divide both sides by -3.<BR>\n" );
document.write( "y = 12/(-3)<BR>\n" );
document.write( "y = -4<BR>\n" );
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document.write( "Now we can substitute -4 for y in the first equation, and solve for x.<BR>\n" );
document.write( "4x -  y = -4<BR>\n" );
document.write( "4x - (-4) = -4<BR>\n" );
document.write( "4x + 4 = -4<BR>\n" );
document.write( "4x = -8<BR>\n" );
document.write( "x = -2<BR>\n" );
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document.write( "Since x = -2 and y = -4 our solution is the ordered pair (-2,-4).<BR>\n" );
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document.write( "We should check our work with the original equations. The ordered pair (-2,-4) will make both equations true.<BR>\n" );
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document.write( "4x -  y = -4<BR>\n" );
document.write( "4(-2) - (-4) = -4<BR>\n" );
document.write( "-8 + 4 = -4<BR>\n" );
document.write( "-4 = -4 (true!)<BR>\n" );
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document.write( "12 - 3y = 24<BR>\n" );
document.write( "12 - 3(-4) = 24<BR>\n" );
document.write( "12 - (-12) = 24<BR>\n" );
document.write( "12 + 12 = 24<BR>\n" );
document.write( "24 = 24 (true!)<BR>\n" );
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document.write( "Hope this helps!<BR>\n" );
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document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex </SPAN>\n" );
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