document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203219>Question 203219</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the following system of equations using algebra. state whether the system is consistent/ inconsistent and dependent/independent.<BR>\n" );
document.write( "3x-2y=7<BR>\n" );
document.write( "4y=6x+10<BR>\n" );
document.write( "so, I found points for each equation and graphed them. I found that the two equations are parallel to each other, so the would be inconsistent/independent- there are no solutions<BR>\n" );
document.write( "is that right? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153327 by </B><A HREF=/tutors/aboutme.mpl?userid=PRMath><B>PRMath(133)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=PRMath><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=153327\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> solve the following system of equations using algebra. state whether the system is consistent/ inconsistent and dependent/independent.<BR>\n" );
document.write( "3x-2y=7<BR>\n" );
document.write( "4y=6x+10<BR>\n" );
document.write( "so, I found points for each equation and graphed them. I found that the two equations are parallel to each other, so the would be inconsistent/independent- there are no solutions<BR>\n" );
document.write( "is that right?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You are correct that these equations form parallel lines.  How do I know that without graphing?  Well, I solved for \"y\" in each equation, so that I could see the equation in a y = mx + b format.  In this format, I can easily see the slope (which is the 'm' in the equation) and in each case, the slope was 3/2.  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "When slopes are equal, the lines are parallel. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "When you have parallel lines, the system is INCONSISTENT (so you were correct) because there is NO SOLUTION (you were correct again!) :-)   And yes, since the equations are not equivalent, they are INDEPENDENT.  So you were correct on all 3 counts.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now my question to you is:  You said you solved this by graphing both lines.  The directions, however, wanted you to solve this system algebraically.  Do you know how to do that?   If not, re-post and I'm sure someone will show you how to solve a system without having to find points on each equation and graphing.  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "However.... you did get a correct answer by your method so good for you! :-)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I hope this helps. :-) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );