document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=650978>Question 650978</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hi,im a student 15 years old, having trouble with finding the solution to this question.\r<BR>\n" );
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document.write( "6x + 5y = 7      &        x - y = 3 \r<BR>\n" );
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document.write( "i have to find the coordinates (x,y) i found that the answer is x= 2 and y = -1 <BR>\n" );
document.write( "but i dont know how to find the soulution. Please help thanks.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #407533 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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=407533\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Good point,\" I have the answer but not the solution.\" I wish all my students would realize the difference. By the way, the point (2,-1) is correct. There are a at least two ways to solve the problem, I'll show you the one called,\"solve by substitution.\" You are given two equations in two variables, x and y,<BR>\n" );
document.write( "(1) 6x + 5y = 7 and<BR>\n" );
document.write( "(2) x - y = 3<BR>\n" );
document.write( "Your first step is to solve one of the equations for one of the variable in terms of the other variable. Since (2) is simpler than (1), let's solve (2) for x, yielding<BR>\n" );
document.write( "(3) x = 3 + y, OK?<BR>\n" );
document.write( "Now we substitute (3) into (1), ergo the substitution method, and get<BR>\n" );
document.write( "(4) 6*(3 + y) + 5y = 7; note that you now have only one equation in a single variable.<BR>\n" );
document.write( "Simplify (4) to get<BR>\n" );
document.write( "(5) 18 + 6y + 5y = 7 or<BR>\n" );
document.write( "(6) 11y = -11, OK? Then<BR>\n" );
document.write( "(7) y = -1<BR>\n" );
document.write( "Now put y = -1 into (2) and get<BR>\n" );
document.write( "(8) x - (-1) = 3 or<BR>\n" );
document.write( "(9) x = 2<BR>\n" );
document.write( "Our point is (2,-1), but is it correct?<BR>\n" );
document.write( "Now always check your answer! Since we used (2) to derive the value of x, check the solution with (1).<BR>\n" );
document.write( "Is (6*(2) + 5*(-1) = 7)?<BR>\n" );
document.write( "Is (12 - 5 = 7)?<BR>\n" );
document.write( "Is (7 = 7)? Yes<BR>\n" );
document.write( "Answer: The solution pair is (2,-1)<BR>\n" );
document.write( "Make sense? To apply the substitution method you must be adept at simplifying algebraic equations. Otherwise it's straight forward.\r<BR>\n" );
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