document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=969294>Question 969294</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve and CHECK the system of equations by either substitution or addition method. PLEASE! SHOW ALL WORK AND EVERY STEP.  State what method you used and then show what  x and Y=\r<BR>\n" );
document.write( "\n" );
document.write( "3x=-4y+15<BR>\n" );
document.write( "8y=-6x+30 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #592208 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=592208\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's isolate the y variable, since 4 and 8 are factors.  We could also do it with x, since 3 and 6 are factors.\r<BR>\n" );
document.write( "\n" );
document.write( "the top equation becomes 3x-15=-4y<BR>\n" );
document.write( "the bottom equation     -6x+30=8y     I moved the y to the right side and the x and constant to the left.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Notice that if we multiply the top equation by 2, we will have -8y on the right in the first and +8y on the right in the second.\r<BR>\n" );
document.write( "\n" );
document.write( "These will add to zero.\r<BR>\n" );
document.write( "\n" );
document.write( "2(3x-15=-4y)  is 6x-30=-8y<BR>\n" );
document.write( "      Bottom    -6x+30=8y\r<BR>\n" );
document.write( "\n" );
document.write( "These add to zero  0+0=0<BR>\n" );
document.write( "The two equations are identical.  That means that either one may be used to show the relation between y and x.\r<BR>\n" );
document.write( "\n" );
document.write( "Using the bottom equation, dividing both sides by 8<BR>\n" );
document.write( "(-6/8)x +(30/8)=8y/8\r<BR>\n" );
document.write( "\n" );
document.write( "(-3/4)x + (15/4)=y\r<BR>\n" );
document.write( "\n" );
document.write( "This is a line with y-intercept (15/4), or 3.75 and slope -(3/4).  Anything on that line will be a solution for x and y, such as x=0 y=3.75  or y=0 x=5.\r<BR>\n" );
document.write( "\n" );
document.write( "Stated another way, there are an infinite number of solutions, which fall along the infinite number of points on a line.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );