document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=828304>Question 828304</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3 systems of 2 equations/inequalities   y=2x+1     y= -6x      y=3x+1                                                                                                                                                             use each method to solve 1 system    [a] graphing   [b] substitution  [c]  elimination                                                                                                                                                          find a system that has each of the following   coincident lines,intersecting lines,parallel lines,perpendicular lines                                                                                                                                                                 explain reasoning </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #499220 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=499220\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ---<BR>\n" );
document.write( "given:<BR>\n" );
document.write( "y = 2x + 1<BR>\n" );
document.write( "y = -6x<BR>\n" );
document.write( "y = 3x + 1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "by observation, the three linear equations are all mutually intersecting, because they all have different slopes.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the three equations give rise to three possible linear systems of two equations each.<BR>\n" );
document.write( "I will solve one of those systems, and you can do the rest:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "y = 2x + 1<BR>\n" );
document.write( "y = 3x + 1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "put the system of linear equations into standard form:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "2x - y = -1<BR>\n" );
document.write( "3x - y = -1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "copy and paste the above linear system in standard form into this matrix-method solver:<BR>\n" );
document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "solution by matrix method:<BR>\n" );
document.write( "x = 0<BR>\n" );
document.write( "y = 1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "system matrix<BR>\n" );
document.write( "2 -1<BR>\n" );
document.write( "3 -1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "inverse of system matrix<BR>\n" );
document.write( "-1 1<BR>\n" );
document.write( "-3 2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "determinant of system matrix = 1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "now by elimination method:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "y = 2x + 1<BR>\n" );
document.write( "(y = 3x + 1) * -1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "y = 2x + 1<BR>\n" );
document.write( "-y = -3x + -1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "add the system:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "-x = 0<BR>\n" );
document.write( "x = 0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "y = 2x + 1<BR>\n" );
document.write( "y = 2(0) + 1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "y = 1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "solution by elimination method:<BR>\n" );
document.write( "x = 0<BR>\n" );
document.write( "y = 1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the method agree.<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<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );