document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=617761>Question 617761</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Without graphing answer the following questions about the system:\r<BR>\n" );
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document.write( "4x+y=7<BR>\n" );
document.write( "32x-56=-8y\r<BR>\n" );
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document.write( "Does the system have one solution, no solution or an infinite number of solutions? Is the system incosistent, are the equations dependent, or neither? <BR>\n" );
document.write( "What does the eqation look like? Does it have one line, parallel lines or intersecting lines? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #388536 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=388536\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equations are:<BR>\n" );
document.write( "4x+y=7<BR>\n" );
document.write( "32x-56=-8y <BR>\n" );
document.write( "solve for y in both equations to put them both in the slope intercept form for linear equations of y = mx + b<BR>\n" );
document.write( "m is the slope and b is the y intercepts.<BR>\n" );
document.write( "the first equation is:<BR>\n" );
document.write( "4x + y = 7<BR>\n" );
document.write( "subtract 4x from both sides of the equation to getr:<BR>\n" );
document.write( "y = -4x + 7<BR>\n" );
document.write( "the slope is -4<BR>\n" );
document.write( "the y intercept is 7<BR>\n" );
document.write( "the second equation is:<BR>\n" );
document.write( "32x - 56 = -8y<BR>\n" );
document.write( "add 8y to both sides of the equation to get:<BR>\n" );
document.write( "8y + 32x - 56 = 0<BR>\n" );
document.write( "subtract 32x and add 56 from both sides of the equation to get:<BR>\n" );
document.write( "8y = -32x + 56<BR>\n" );
document.write( "divide both sides of the equation by 8 to get:<BR>\n" );
document.write( "y = -32x/8 + 56/8<BR>\n" );
document.write( "simplify this to get:<BR>\n" );
document.write( "y = -4x + 7<BR>\n" );
document.write( "the equations are identical.<BR>\n" );
document.write( "they have the same slope and the same y intercept<BR>\n" );
document.write( "if you graph them they will look like the same line.<BR>\n" );
document.write( "the system of equations has an infinite number of solutions because the lines are identical and they coincide completely with each other.<BR>\n" );
document.write( "in the standard form for the equation of a straight line, if the equations are exact multiples of each other, then they are identical.<BR>\n" );
document.write( "in the standard form, you get:<BR>\n" );
document.write( "4x + y = 7 (already in standard form)<BR>\n" );
document.write( "32x + 8y = 56 (converted to standard form_)<BR>\n" );
document.write( "32x / 4x = 8<BR>\n" );
document.write( "8y / y = 8<BR>\n" );
document.write( "56 / 7 = 8<BR>\n" );
document.write( "since each term in the equations have the same ratio, then the equations are in proportion and are therefore identical to each other.<BR>\n" );
document.write( "when you place them in the slope intercept form of the equation, they become identical meaning they are the same line.<BR>\n" );
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