document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=822059>Question 822059</A>: <I><SPAN STYLE=\"word-break: break-all;\"> given the equation 3x+9y=-8, write a second linear equation to create a system that:<BR>\n" );
document.write( "• has exactly one solution. Explain your reasoning<BR>\n" );
document.write( "• has no solution. Explain your reasoning<BR>\n" );
document.write( "• has infinitely many solutions. Explain your reasoning\r<BR>\n" );
document.write( "\n" );
document.write( "• interpret the meaning of the solution, if it exist, in the context of the graph of the following system if equations. <BR>\n" );
document.write( "-5x+2y=10<BR>\n" );
document.write( "10x-4y=20 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #494565 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=494565\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ---<BR>\n" );
document.write( "original, standard form: ax + by = c<BR>\n" );
document.write( "3x + 9y = -8<BR>\n" );
document.write( "slope = -a/b = -3/9 = -1/3<BR>\n" );
document.write( "y-intercept = c/b = -8/9<BR>\n" );
document.write( "---<BR>\n" );
document.write( "write second linear equation where the system has only one solution:<BR>\n" );
document.write( "3x + 9y = -8<BR>\n" );
document.write( "9x - 3y = -8<BR>\n" );
document.write( "slope = -a/b = -9/-3 = 3<BR>\n" );
document.write( "y-intercept = c/b = -8/-3 = 8/3<BR>\n" );
document.write( "reason: slopes are negative reciprocal, so the lines are perpendicular and must have a unique solution, in this case the solution is:<BR>\n" );
document.write( "x= -1.06666667<BR>\n" );
document.write( "y= -0.533333333<BR>\n" );
document.write( "---<BR>\n" );
document.write( "write second linear equation where the system has no solution:<BR>\n" );
document.write( "3x + 9y = -8<BR>\n" );
document.write( "3x + 9y = 0<BR>\n" );
document.write( "slope = -a/b = -3/9 = -1/3<BR>\n" );
document.write( "y-intercept = c/b = 0/9 = 0<BR>\n" );
document.write( "reason: slopes are equal, so the lines are parallel, but they have distinct y-intercepts so the lines have no common solution because they never intersect<BR>\n" );
document.write( "---<BR>\n" );
document.write( "write second linear equation where the system has infinitely many solutions:<BR>\n" );
document.write( "3x + 9y = -8<BR>\n" );
document.write( "6x + 18y = -16<BR>\n" );
document.write( "slope = -a/b = -6/18 = -1/3<BR>\n" );
document.write( "y-intercept = c/b = -16/18 = -8/9<BR>\n" );
document.write( "reason: slopes are equal, so the lines are parallel, and their y-intercepts are equal, so the lines are coincident, hence have an infinite number of solutions<BR>\n" );
document.write( "---<BR>\n" );
document.write( "-5x + 2y = 10<BR>\n" );
document.write( "10x - 4y = 20<BR>\n" );
document.write( "the lines have equal slopes (5/2), so the lines are parallel, but different y-intercepts (5) and (-5), so they do not intercept and hence have no common solution<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve and graph linear equations:<BR>\n" );
document.write( "https://sooeet.com/math/linear-equation-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve quadratic equations, quadratic formula:<BR>\n" );
document.write( "https://sooeet.com/math/quadratic-formula-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve systems of linear equations up to 6-equations 6-variables:<BR>\n" );
document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );