document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=827059>Question 827059</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do we graph the system 2x + 2y = 4  AND 12 - 3x = 3y? Need to determine if there is 1 solution, Infinite solutions, or No solution.  Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #498428 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=498428\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ---<BR>\n" );
document.write( "2x + 2y = 4<BR>\n" );
document.write( "12 - 3x = 3y<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 + 2y = 4<BR>\n" );
document.write( "3x + 3y = 12<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:<BR>\n" );
document.write( "This linear system is singular. It has no solution<BR>\n" );
document.write( "---<BR>\n" );
document.write( "system matrix<BR>\n" );
document.write( "2 2<BR>\n" );
document.write( "3 3<BR>\n" );
document.write( "---<BR>\n" );
document.write( "determinant of system matrix = 0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "The linear system has no solution because the lines are parallel, as you can see in the graph below:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "graph:<BR>\n" );
document.write( "2x + 2y = 4<BR>\n" );
document.write( "3x + 3y = 12<BR>\n" );
document.write( "---<BR>\n" );
document.write( "2y = -2x + 4<BR>\n" );
document.write( "3y = -3x + 12<BR>\n" );
document.write( "---<BR>\n" );
document.write( "y = -x + 2<BR>\n" );
document.write( "y = -x + 4<BR>\n" );
document.write( "---<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+-x+%2B+2%2C+-x+%2B+4%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+-x+%2B+2%2C+-x+%2B+4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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" );