document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189987>Question 189987</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help I have tried and cant come up with the solution.\r<BR>\n" );
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document.write( ".  Find the equation, in standard form, of the line perpendicular to 2x - 3y = -5 and passing through (3, -2). Write the equation in standard form, with all integer coefficients. \r<BR>\n" );
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document.write( "2x-3y= -5  and write in standard form which is Ax+By=C now to break it down.\r<BR>\n" );
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document.write( "A=2x,B=3y,C=-5\r<BR>\n" );
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document.write( "2x+(-3)y=-5\r<BR>\n" );
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document.write( "4.  Solve the system of equations using the substitution method.<BR>\n" );
document.write( "If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is \"no solution\" or \"infinitely many solutions\" and state how you arrived at that conclusion.<BR>\n" );
document.write( "     3x + y = 2<BR>\n" );
document.write( "     2x - y = 3\r<BR>\n" );
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document.write( "5.  Solve the system of equations using the addition (elimination) method.<BR>\n" );
document.write( "If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is \"no solution\" or \"infinitely many solutions\" and state how you arrived at that conclusion.<BR>\n" );
document.write( "      3x - 11y = 9<BR>\n" );
document.write( "     -9x + 33y = -27\r<BR>\n" );
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document.write( "6.  Solve the system of equations using the addition (elimination) method.<BR>\n" );
document.write( "If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is \"no solution\" or \"infinitely many solutions\" and state how you arrived at that conclusion.<BR>\n" );
document.write( "     4x + 10y = 2<BR>\n" );
document.write( "     3x + 5y = 5\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142660 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=142660\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Please help I have tried and cant come up with the solution.<BR>\n" );
document.write( ". Find the equation, in standard form, of the line perpendicular to 2x - 3y = -5 and passing through (3, -2). Write the equation in standard form, with all integer coefficients.<BR>\n" );
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document.write( "First we have to find the slopes, we need it in the slope intercept form for this:<BR>\n" );
document.write( "2x - 3y = -5; this is the standard form<BR>\n" );
document.write( "-3y = -2x - 5<BR>\n" );
document.write( "Get rid of all those negatives, multiply eq by -1<BR>\n" );
document.write( "3y = 2x + 5<BR>\n" );
document.write( "Divide by 3 to get y<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F3 ALIGN=MIDDLE  ALT=\"5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The slope of this equation (m1) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Find the slope (m2) of the perpendicular line:  m1*m2 = -1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >*m2 = -1<BR>\n" );
document.write( "m2 = -1 * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "m2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the slope of the perpendicular line<BR>\n" );
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document.write( "It passes thru 3,-2 write the equation using the point/slope form y-y1 = m(x-x1)<BR>\n" );
document.write( "y - (-2) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >(x - 3)<BR>\n" );
document.write( "y + 2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F2 ALIGN=MIDDLE  ALT=\"9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F2 ALIGN=MIDDLE  ALT=\"9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > - 2<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F2 ALIGN=MIDDLE  ALT=\"9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F2 ALIGN=MIDDLE  ALT=\"4%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F2 ALIGN=MIDDLE  ALT=\"5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the equation<BR>\n" );
document.write( "To put it in the standard form, multiply equation by 2<BR>\n" );
document.write( "2y = -3x + 5<BR>\n" );
document.write( "+3x + 2y = 5 is the standard form of the perpendicular line<BR>\n" );
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document.write( "Check it using the given coordinates 3, -2<BR>\n" );
document.write( "3(3) + 2(-2) = 5<BR>\n" );
document.write( "9 - 4 = 5, confirms our equation<BR>\n" );
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document.write( "4. Solve the system of equations using the substitution method.<BR>\n" );
document.write( "If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is \"no solution\" or \"infinitely many solutions\" and state how you arrived at that conclusion.<BR>\n" );
document.write( "3x + y = 2<BR>\n" );
document.write( "2x - y = 3<BR>\n" );
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document.write( "Use the 1st equation for substitution <BR>\n" );
document.write( "y = -3x + 2<BR>\n" );
document.write( "Substitute (-3x+2) for y in the 2nd equation<BR>\n" );
document.write( "2x - (-3x+2) = 3<BR>\n" );
document.write( "2x + 3x - 2 = 3; minus a minus is a plus<BR>\n" );
document.write( "5x = 3 + 1<BR>\n" );
document.write( "5x = 5<BR>\n" );
document.write( "x = 1<BR>\n" );
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document.write( "Substitute 1 for x in the 1st equation find y<BR>\n" );
document.write( "3(1) + y = 2<BR>\n" );
document.write( "3 + y = 2<BR>\n" );
document.write( "y = 2 - 3<BR>\n" );
document.write( "y = -1<BR>\n" );
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document.write( "Check solutions in the 2nd equation (2x - y = 3)<BR>\n" );
document.write( "2(1) - (-1) = 3<BR>\n" );
document.write( "2 + 1 = 3; confirms our solutions, ordered pair: 1, -1<BR>\n" );
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document.write( "5. Solve the system of equations using the addition (elimination) method.<BR>\n" );
document.write( "If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is \"no solution\" or \"infinitely many solutions\" and state how you arrived at that conclusion.<BR>\n" );
document.write( "3x - 11y = 9<BR>\n" );
document.write( "-9x + 33y = -27<BR>\n" );
document.write( "multiply the 1st equation by 3, add to the 2nd equation<BR>\n" );
document.write( "+9x - 33y = 27<BR>\n" );
document.write( "-9x + 33y = -27<BR>\n" );
document.write( "-------------------adding eliminates everything, there is no solution<BR>\n" );
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document.write( "6. Solve the system of equations using the addition (elimination) method.<BR>\n" );
document.write( "If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is \"no solution\" or \"infinitely many solutions\" and state how you arrived at that conclusion.<BR>\n" );
document.write( "4x + 10y = 2<BR>\n" );
document.write( "3x + 5y = 5 <BR>\n" );
document.write( "Multiply the 2nd equation by -2 add to the 1st equation<BR>\n" );
document.write( "+4x + 10y = 2<BR>\n" );
document.write( "-6x - 10y = -10<BR>\n" );
document.write( "------------------adding eliminates y, find x<BR>\n" );
document.write( "-2x = -8<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-8%29%2F%28-2%29 ALIGN=MIDDLE  ALT=\"%28-8%29%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "x = +4<BR>\n" );
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document.write( "Find y using the 1st equation<BR>\n" );
document.write( "4(4) + 10y = 2<BR>\n" );
document.write( "16 + 10y = 2<BR>\n" );
document.write( "10y = 2 - 16<BR>\n" );
document.write( "10y = -14<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-14%29%2F10 ALIGN=MIDDLE  ALT=\"%28-14%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = -1.4<BR>\n" );
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document.write( "Check solution in the 2nd equation:<BR>\n" );
document.write( "3(4) + 5(-1.4) = 5<BR>\n" );
document.write( "12 - 7 = 5; confirms our solutions, ordered pair: 4, -1.4<BR>\n" );
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