document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=932576>Question 932576</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Not every system of linear equations has a single solution. Try to make a sketch of a system of linear equations that does not have a single solution. Compare the equations of these <BR>\n" );
document.write( "systems. What is true of their slopes?...y-intercepts?...etc… </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #566310 by </B><A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><B>TimothyLamb(4379)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><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=TimothyLamb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=566310\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a system of linear equations can only have multiple solutions if all of the equations are coincident, in which case the system has infinitely many solutions<BR>\n" );
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document.write( "two linear equations are coincident if their graphs lie on top of each other<BR>\n" );
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document.write( "if two linear equations are coincident they have the same slope and the same y-intercept<BR>\n" );
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document.write( "we can build such a system very easily:<BR>\n" );
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document.write( "invent one linear equation:<BR>\n" );
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document.write( "y = 3x + 5<BR>\n" );
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document.write( "find the slope and y-intercept of this equation:<BR>\n" );
document.write( "slope = 3<BR>\n" );
document.write( "y-intercept = 5<BR>\n" );
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document.write( "to make another linear equation coincident with the above equation, multiply the above equation by any real number other than 1<BR>\n" );
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document.write( "for example:<BR>\n" );
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document.write( "-2.5*(y = 3x + 5)<BR>\n" );
document.write( "-2.5y = -2.5*3x - 2.5*5<BR>\n" );
document.write( "-2.5y = -7.5x - 12.5<BR>\n" );
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document.write( "find the slope and y-intercept of the second equation:<BR>\n" );
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document.write( "-2.5y = -7.5x - 12.5<BR>\n" );
document.write( "y = (-7.5x - 12.5)/-2.5<BR>\n" );
document.write( "y = 3x + 5<BR>\n" );
document.write( "slope = 3<BR>\n" );
document.write( "y-intercept = 5<BR>\n" );
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document.write( "answer:<BR>\n" );
document.write( "if two linear equations have multiple solutions they must have the same slope and the same y-intercept<BR>\n" );
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document.write( "Solve and graph linear equations:<BR>\n" );
document.write( "https://sooeet.com/math/linear-equation-solver.php<BR>\n" );
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document.write( "Solve quadratic equations, quadratic formula:<BR>\n" );
document.write( "https://sooeet.com/math/quadratic-formula-solver.php<BR>\n" );
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document.write( "Convert fractions, decimals, and percents:<BR>\n" );
document.write( "https://sooeet.com/math/fraction-decimal-percent.php<BR>\n" );
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document.write( "Calculate and graph the linear regression of any data set:<BR>\n" );
document.write( "https://sooeet.com/math/linear-regression.php </SPAN>\n" );
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