document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=82049>Question 82049</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0072549017/algebrahomeworkh>beginners algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Find the values for m and b in the following system so that the solution to the system is (-3,4)<BR>\n" );
document.write( "5x+7y=b<BR>\n" );
document.write( "mx+y=22\r<BR>\n" );
document.write( "\n" );
document.write( "Please, and thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #58804 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=58804\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The solution to the system means that the point (-3, 4) satisfies both of the equations.<BR>\n" );
document.write( "So you can substitute these values for x and y (x equals -3 and y equals +4) into both of <BR>\n" );
document.write( "the equations, and solve for the values of b and m.  <BR>\n" );
document.write( ".<BR>\n" );
document.write( "First go to the equation:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "5x + 7y = b<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Substitute -3 for x and + 4 for y.  When you do that the equation becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "5(-3) + 7(4) = b<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Multiply out the left side to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "-15 + 28 = b<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Add the two terms on the left side and the equation becomes 13 = b.  You now know the <BR>\n" );
document.write( "value of b.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Next go to the second equation:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "mx + y = 22<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Again substitute -3 for x and +4 for y.  When you do the equation becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "m(-3) + 4 = 22<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Get rid of the +4 on the left side by subtracting 4 from both sides.  When you do that<BR>\n" );
document.write( "the equation simplifies to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "m(-3) = 18<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now solve for m by dividing both sides of the equation by -3 (the multiplier of m). When <BR>\n" );
document.write( "you do that division the equation becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "m = 18/-3 = -6<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So the answers to the problem are b = 13 and m = -6<BR>\n" );
document.write( ".<BR>\n" );
document.write( "A way you can check these two values is to put them into the original equations and solve <BR>\n" );
document.write( "for the set to see if the common solution is (-3, 4).  In other words, solve the set:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "5x + 7y = 13 and<BR>\n" );
document.write( "-6x + y = 22<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let's do it by variable elimination.  Multiply the top equation (all terms on both sides)<BR>\n" );
document.write( "by 6 and the bottom equation (all terms on both sides) by 5. When you do that the <BR>\n" );
document.write( "equation set becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "+30x + 42y =  78<BR>\n" );
document.write( "-30x +  5y = 110<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Add the columns in these two equations. Note that this causes the +30x and the -30x to<BR>\n" );
document.write( "cancel. The remaining additions in columns results in:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "47y = 188<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Solve for y by dividing both sides of this equation by 47 to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "y = 188/47 = 4<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now return to either of the equations in which the values of b and m had been substituted.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let's select the equation -6x + y = 22.  We know that y = 4, so substitute that value for y<BR>\n" );
document.write( "and solve for x.  Substituting for y the equation becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "-6x + 4 = 22<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Subtract 4 from both sides:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "-6x = 18<BR>\n" );
document.write( ".<BR>\n" );
document.write( "and divide both sides by -6 to get: x = 18/-6 = -3.  So the coordinate point that satisfies<BR>\n" );
document.write( "the equation set is (-3, + 4) just as the problem said it was.  So our answers for m and b<BR>\n" );
document.write( "check out.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this gives you some insight into the problem and how to solve it<BR>\n" );
document.write( ". </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );