document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=389005>Question 389005</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5r - 9s = -37<BR>\n" );
document.write( "9r + 5s = 103<BR>\n" );
document.write( "solve using elimination method </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #275474 by </B><A HREF=/tutors/aboutme.mpl?userid=haileytucki><B>haileytucki(390)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=haileytucki><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=haileytucki><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=275474\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 5r-9s=-37,9r+5s=103\r<BR>\n" );
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document.write( "Since -9s does not contain the variable to solve for, move it to the right-hand side of the equation by adding 9s to both sides.<BR>\n" );
document.write( "5r=9s-37_9r+5s=103\r<BR>\n" );
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document.write( "Divide each term in the equation by 5.<BR>\n" );
document.write( "(5r)/(5)=(9s)/(5)-(37)/(5)_9r+5s=103\r<BR>\n" );
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document.write( "Simplify the left-hand side of the equation by canceling the common factors.<BR>\n" );
document.write( "r=(9s)/(5)-(37)/(5)_9r+5s=103\r<BR>\n" );
document.write( "\n" );
document.write( "Combine the numerators of all expressions that have common denominators.<BR>\n" );
document.write( "r=(9s-37)/(5)_9r+5s=103\r<BR>\n" );
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document.write( "Replace all occurrences of r with the solution found by solving the last equation for r.  In this case, the value substituted is ((9s-37))/(5).<BR>\n" );
document.write( "r=(9s-37)/(5)_9((9s-37)/(5))+5s=103\r<BR>\n" );
document.write( "\n" );
document.write( "Remove the parentheses around the expression 9s-37.<BR>\n" );
document.write( "r=(9s-37)/(5)_9((9s-37)/(5))+5s=103\r<BR>\n" );
document.write( "\n" );
document.write( "Divide each term in the numerator by the denominator.<BR>\n" );
document.write( "r=(9s)/(5)-(37)/(5)_9((9s-37)/(5))+5s=103\r<BR>\n" );
document.write( "\n" );
document.write( "Remove the parentheses around the expression 9s-37.<BR>\n" );
document.write( "r=(9s)/(5)-(37)/(5)_9((9s-37)/(5))+5s=103\r<BR>\n" );
document.write( "\n" );
document.write( "Divide each term in the numerator by the denominator.<BR>\n" );
document.write( "r=(9s)/(5)-(37)/(5)_9((9s)/(5)-(37)/(5))+5s=103\r<BR>\n" );
document.write( "\n" );
document.write( "Combine the numerators of all expressions that have common denominators.<BR>\n" );
document.write( "r=(9s)/(5)-(37)/(5)_9((9s-37)/(5))+5s=103\r<BR>\n" );
document.write( "\n" );
document.write( "Divide each term in the numerator by the denominator.<BR>\n" );
document.write( "r=(9s)/(5)-(37)/(5)_9((9s)/(5)-(37)/(5))+5s=103\r<BR>\n" );
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document.write( "Multiply 9 by each term inside the parentheses.<BR>\n" );
document.write( "r=(9s)/(5)-(37)/(5)_(81s-333)/(5)+5s=103\r<BR>\n" );
document.write( "\n" );
document.write( "Divide each term in the numerator by the denominator.<BR>\n" );
document.write( "r=(9s)/(5)-(37)/(5)_(81s)/(5)-(333)/(5)+5s=103\r<BR>\n" );
document.write( "\n" );
document.write( "Combine the numerators of all expressions that have common denominators.<BR>\n" );
document.write( "r=(9s)/(5)-(37)/(5)_(81s-333)/(5)+5s=103\r<BR>\n" );
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document.write( "Factor out the GCF of 9 from each term in the polynomial.<BR>\n" );
document.write( "r=(9s)/(5)-(37)/(5)_(9(9s)+9(-37))/(5)+5s=103\r<BR>\n" );
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document.write( "Factor out the GCF of 9 from 81s-333.<BR>\n" );
document.write( "r=(9s)/(5)-(37)/(5)_(9(9s-37))/(5)+5s=103\r<BR>\n" );
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document.write( "Multiply each term by a factor of 1 that will equate all the denominators.  In this case, all terms need a denominator of 5.<BR>\n" );
document.write( "r=(9s)/(5)-(37)/(5)_(9(9s-37))/(5)+5s*(5)/(5)=103\r<BR>\n" );
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document.write( "Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 5.<BR>\n" );
document.write( "r=(9s)/(5)-(37)/(5)_(9(9s-37))/(5)+(5s*5)/(5)=103\r<BR>\n" );
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document.write( "Multiply 5s by 5 to get 25s.<BR>\n" );
document.write( "r=(9s)/(5)-(37)/(5)_(9(9s-37))/(5)+(25s)/(5)=103\r<BR>\n" );
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document.write( "The numerators of expressions that have equal denominators can be combined.  In this case, (9(9s-37))/(5) and ((25s))/(5) have the same denominator of 5, so the numerators can be combined.<BR>\n" );
document.write( "r=(9s)/(5)-(37)/(5)_(9(9s-37)+(25s))/(5)=103\r<BR>\n" );
document.write( "\n" );
document.write( "Simplify the numerator of the expression.<BR>\n" );
document.write( "r=(9s)/(5)-(37)/(5)_(81s-333+25s)/(5)=103\r<BR>\n" );
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document.write( "Since 81s and 25s are like terms, add 25s to 81s to get 106s.<BR>\n" );
document.write( "r=(9s)/(5)-(37)/(5)_(106s-333)/(5)=103\r<BR>\n" );
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document.write( "Multiply each term in the equation by 5.<BR>\n" );
document.write( "r=(9s)/(5)-(37)/(5)_(106s-333)/(5)*5=103*5\r<BR>\n" );
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document.write( "Simplify the left-hand side of the equation by canceling the common factors.<BR>\n" );
document.write( "r=(9s)/(5)-(37)/(5)_106s-333=103*5\r<BR>\n" );
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document.write( "Multiply 103 by 5 to get 515.<BR>\n" );
document.write( "r=(9s)/(5)-(37)/(5)_106s-333=515\r<BR>\n" );
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document.write( "Since -333 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 333 to both sides.<BR>\n" );
document.write( "r=(9s)/(5)-(37)/(5)_106s=333+515\r<BR>\n" );
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document.write( "Add 515 to 333 to get 848.<BR>\n" );
document.write( "r=(9s)/(5)-(37)/(5)_106s=848\r<BR>\n" );
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document.write( "Divide each term in the equation by 106.<BR>\n" );
document.write( "r=(9s)/(5)-(37)/(5)_(106s)/(106)=(848)/(106)\r<BR>\n" );
document.write( "\n" );
document.write( "Simplify the left-hand side of the equation by canceling the common factors.<BR>\n" );
document.write( "r=(9s)/(5)-(37)/(5)_s=(848)/(106)\r<BR>\n" );
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document.write( "Simplify the right-hand side of the equation by simplifying each term.<BR>\n" );
document.write( "r=(9s)/(5)-(37)/(5)_s=8\r<BR>\n" );
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document.write( "Replace all occurrences of s with the solution found by solving the last equation for s.  In this case, the value substituted is 8.<BR>\n" );
document.write( "r=(9(8))/(5)-(37)/(5)_s=8\r<BR>\n" );
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document.write( "Multiply 9 by 8 in the numerator.<BR>\n" );
document.write( "r=(9*8)/(5)-(37)/(5)_s=8\r<BR>\n" );
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document.write( "Multiply 9 by 8 to get 72.<BR>\n" );
document.write( "r=(72)/(5)-(37)/(5)_s=8\r<BR>\n" );
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document.write( "Complete the multiplication to produce a denominator of 5 in each expression.<BR>\n" );
document.write( "r=-(37)/(5)+(72)/(5)_s=8\r<BR>\n" );
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document.write( "Combine the numerators of all fractions that have common denominators.<BR>\n" );
document.write( "r=(-37+72)/(5)_s=8\r<BR>\n" );
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document.write( "Add 72 to -37 to get 35.<BR>\n" );
document.write( "r=(35)/(5)_s=8\r<BR>\n" );
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document.write( "Reduce the expression (35)/(5) by removing a factor of 5 from the numerator and denominator.<BR>\n" );
document.write( "r=7_s=8\r<BR>\n" );
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document.write( "This is the solution to the system of equations.<BR>\n" );
document.write( "r=7_s=8 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );