document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=243280>Question 243280</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve and determine whether each system has no solution, one solution or an infinite number of solutions show why<BR>\n" );
document.write( "y=4x+6<BR>\n" );
document.write( "8x-y= -7 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #178229 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=178229\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y = mx + b is the basic linear equation.<BR>\n" );
document.write( "...<BR>\n" );
document.write( "EQ 1:  y = 4x + 6, which is already in this form.<BR>\n" );
document.write( "m = 4, which is the slope<BR>\n" );
document.write( "y-intercept = 6<BR>\n" );
document.write( "x-intercept = -3/2, which can be demonstrated by 4*(-3/2) + 6 = 0<BR>\n" );
document.write( "...<BR>\n" );
document.write( "EQ 2:  8x - y = -7, which needs to be shaped up algebraically.<BR>\n" );
document.write( "Add y to both sides<BR>\n" );
document.write( "8x = -7 + y = y - 7<BR>\n" );
document.write( "Add 7 to both sides<BR>\n" );
document.write( "8x + 7 = y<BR>\n" );
document.write( "y = 8x + 7<BR>\n" );
document.write( "m = 8, which is twice a great a slope as EQ 1<BR>\n" );
document.write( "y-intercept = 7<BR>\n" );
document.write( "x-intercept = -7/8<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Now graph the two equations.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Agraph%28500%2C500%2C-10%2C10%2C-10%2C10%2C4%2Ax%2B6%2C+8%2Ax%2B7%29%0D%0A ALIGN=MIDDLE  ALT=\"%0D%0Agraph%28500%2C500%2C-10%2C10%2C-10%2C10%2C4%2Ax%2B6%2C+8%2Ax%2B7%29%0D%0A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...<BR>\n" );
document.write( "There is one solution, as can be seen in the graph. <BR>\n" );
document.write( "...<BR>\n" );
document.write( "To demonstrate algebraically there is one solution, recall that equal things are equal.  y=y is self-evident, so you can set the two equations equal to one another and solve them.<BR>\n" );
document.write( "...<BR>\n" );
document.write( "8x + 7 = 4x + 6<BR>\n" );
document.write( "Subtract 4x from both sides<BR>\n" );
document.write( "4x + 7 = 6<BR>\n" );
document.write( "Subtract 7 from both sides<BR>\n" );
document.write( "4x = -1<BR>\n" );
document.write( "Divide both sides by 4<BR>\n" );
document.write( "x = -1/4<BR>\n" );
document.write( "So x=-1/4 is the solution (the unique point where the two equations cross). </SPAN>\n" );
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