document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=63519>Question 63519</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have to solve the problem by using substitution Method. If the problem has no solution or an infinite solution or an answer.\r<BR>\n" );
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document.write( "1. x + 7Y = 16<BR>\n" );
document.write( "   -3X + 6Y= 33\r<BR>\n" );
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document.write( "2. X + Y = 1<BR>\n" );
document.write( "   X + Y = 2\r<BR>\n" );
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document.write( "This problem has to be sloved by equations by any method.<BR>\n" );
document.write( "8x + 9 = -5y<BR>\n" );
document.write( "-3x + 3y = -21\r<BR>\n" );
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document.write( "In a recent game Will scored 42 points on a combination of 18 two and three point baskets. How many shots of each type were made?\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 #44219 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=44219\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> solve the problem by using substitution Method. If the problem has no solution or an infinite solution or an answer. <BR>\n" );
document.write( "1. <BR>\n" );
document.write( "1st: x + 7Y = 16<BR>\n" );
document.write( "2nd: -3X + 6Y= 33<BR>\n" );
document.write( "Solve 1st for x, as follows:<BR>\n" );
document.write( "3rd: x=16-7y<BR>\n" );
document.write( "Substitute into 2nd to solve for y as follows:<BR>\n" );
document.write( "-3(16-7y)+6y=33<BR>\n" );
document.write( "-48+21y+6y=33<BR>\n" );
document.write( "27y=81<BR>\n" );
document.write( "y=3<BR>\n" );
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document.write( "Substitute in 3rd to solve for x, as follows:<BR>\n" );
document.write( "x=16-7(3)<BR>\n" );
document.write( "x=-5<BR>\n" );
document.write( "Check answer in 2nd as follows:<BR>\n" );
document.write( "-3(-5)+6(3)=33<BR>\n" );
document.write( "15+18=33<BR>\n" );
document.write( "33=33<BR>\n" );
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document.write( "2. <BR>\n" );
document.write( "1st: X + Y = 1<BR>\n" );
document.write( "2nd: X + Y = 2 <BR>\n" );
document.write( "Solve 1st for x, as follows:<BR>\n" );
document.write( "x=1-y<BR>\n" );
document.write( "Substitute in 2nd to get:<BR>\n" );
document.write( "(1-y)+y=2<BR>\n" );
document.write( "1=2<BR>\n" );
document.write( "This is a contradiction indicating <BR>\n" );
document.write( "there is no solution to this system<BR>\n" );
document.write( "of equations.  It also means you would<BR>\n" );
document.write( "get two parallel lines that do not meet<BR>\n" );
document.write( "in a point if you were to graph these <BR>\n" );
document.write( "two equations.<BR>\n" );
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document.write( "This problem has to be sloved by equations by any method.<BR>\n" );
document.write( "8x + 9 = -5y<BR>\n" );
document.write( "-3x + 3y = -21 <BR>\n" );
document.write( "Hint:<BR>\n" );
document.write( "Write both equations in the form ax+b=c<BR>\n" );
document.write( "Multiply the 1st by 3 and the 2nd by 8<BR>\n" );
document.write( "Then subtract the 1st from the 2nd.<BR>\n" );
document.write( "Good luck.<BR>\n" );
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document.write( "In a recent game Will scored 42 points on a combination of 18 two and three point baskets. How many shots of each type were made? <BR>\n" );
document.write( "Let # of 2-pt baskets be \"x\"; these are worth 2x points in the game.<BR>\n" );
document.write( "The # of 3-pt baskets is \"18-x\" ; these are worth 3(18-x)=54-3x points.<BR>\n" );
document.write( "EQUATION:<BR>\n" );
document.write( "points + points = 42<BR>\n" );
document.write( "2x+54-3x=42<BR>\n" );
document.write( "-x=-12<BR>\n" );
document.write( "x=12 (# of 2-point baskets)<BR>\n" );
document.write( "18-x=6 (# of 3-point baskets)<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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