document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120951>Question 1120951</A>: <I><SPAN STYLE=\"word-break: break-all;\"> state the number of solutions for the linear system of equations 27x=3y+78 3y=90-6x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #736651 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=736651\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> place these equations in slope intercept form.\r<BR>\n" );
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document.write( "27x = 3y + 78 is the first equation.<BR>\n" );
document.write( "subtract 78 from both sides to get 27x - 78 = 3y<BR>\n" );
document.write( "solve for y to get y = 27x / 3 - 78/3<BR>\n" );
document.write( "simplify to get y = 9x - 26\r<BR>\n" );
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document.write( "3y = 90 - 6x<BR>\n" );
document.write( "rearrange the terms in descending order of degree tp get 3y = -6x + 90<BR>\n" );
document.write( "divide both side by 3 to get y = -6/3 * x + 90/3<BR>\n" );
document.write( "simplify to get y = -2x + 30\r<BR>\n" );
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document.write( "they are now both in slope intercept form of y = mx + b where m is the slope and b is the y-intercept.\r<BR>\n" );
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document.write( "if the slopes are the same and the y-intercepts are the same, the lines are identical and you have an infinite number of possible solutions.\r<BR>\n" );
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document.write( "if the slopes are the same and the y-intercepts are different, the lines are parallel and you have no possible solutions.\r<BR>\n" );
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document.write( "if the slopes are not the same, the lines are not identical or parallel and you have one possible solution.\r<BR>\n" );
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document.write( "these lines do not have the same slope and you therefore have one possible solution.\r<BR>\n" );
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document.write( "i graphed both equations and the graph shows one possible solution.\r<BR>\n" );
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document.write( "the red line is caused by the first equation after it have been placed in slope intercept form.\r<BR>\n" );
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document.write( "the blue line is caused by the second equation after it has been placed in slope intercept form.\r<BR>\n" );
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document.write( "the graph shows one solution at the coordinate point of (5.091,19.818)\r<BR>\n" );
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document.write( "that means x = 5.091 and y = 19.818 is the one common solution to both equations.\r<BR>\n" );
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document.write( "i solved them algebraically and this is what i got.\r<BR>\n" );
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document.write( "start with:\r<BR>\n" );
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document.write( "27x = 3y + 78<BR>\n" );
document.write( "3y = 90 - 6x\r<BR>\n" );
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document.write( "solve for 3y in both equations to get:\r<BR>\n" );
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document.write( "3y = 27x - 78<BR>\n" );
document.write( "3y = -6x + 90\r<BR>\n" );
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document.write( "subtract the second equation from the first to get 0 = 33x - 168\r<BR>\n" );
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document.write( "add 168 to both sides of the equatino to get 168 = 33x\r<BR>\n" );
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document.write( "solve for x to get x = 168 / 33 = 5.090909091\r<BR>\n" );
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document.write( "solve for y in either original equation to get y = 19.81818182\r<BR>\n" );
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document.write( "round to 3 decimal places and you get x = 5.091 and y = 19.818 as shown on the graph.\r<BR>\n" );
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document.write( "here's the graph.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/080509.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "there is only one solution for the system of these two equations.\r<BR>\n" );
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