document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=804939>Question 804939</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the point of intersection/whether the point is a solution for:\r<BR>\n" );
document.write( "\n" );
document.write( "3x + y = 6<BR>\n" );
document.write( "y = -3x + 2\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks. x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #486488 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=486488\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We have two linear equations:<BR>\n" );
document.write( "L1: 3x + y = 6<BR>\n" );
document.write( "L2: y = -3x + 2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "To solve them means to find the point or points of intersection, if any, between L1 and L2.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Substitute (-3x + 2) (the value of y from L2) for y in L1:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "L1: 3x + y = 6<BR>\n" );
document.write( "L1: 3x + (-3x + 2) = 6<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Now solve for x:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "3x - 3x + 2 = 6<BR>\n" );
document.write( "2 = 6<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "The lines L1 and L2 do not intersect.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Check the answer by converting L1 to slope-intercept form: y = mx + b<BR>\n" );
document.write( "---<BR>\n" );
document.write( "L1: 3x + y = 6<BR>\n" );
document.write( "y = -3x + 6<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Now we can see that L1 and L2 have the same slope (-3).<BR>\n" );
document.write( "But L1 and L2 have different y-intercepts (6 for L1 and 2 for L2).<BR>\n" );
document.write( "So L1 and L2 are parallel lines that never intersect.<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( "Convert fractions, decimals, and percents:<BR>\n" );
document.write( "https://sooeet.com/math/fraction-decimal-percent.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Calculate and graph the linear regression of any data set:<BR>\n" );
document.write( "https://sooeet.com/math/linear-regression.php </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );