document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=392551>Question 392551</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve. Use two variables and two equations.\r<BR>\n" );
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document.write( "1.The sum of two numbers is 35. One number is 4 times the other. Find the numbers.\r<BR>\n" );
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document.write( "2.One number is 5 more than another number. The sum of the two numbers is 43. Find the numbers.\r<BR>\n" );
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document.write( "3.One number us 5 times another number. It is also 3 more than twice the other number. Find the numbers.\r<BR>\n" );
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document.write( "4.Ellen is 5 years older than Trudy. Their ages total 39. How old is each person?\r<BR>\n" );
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document.write( "5. In a game of bowling, Buds score was 12 more than Jans. Their combined score was 328. Find their scores. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #278619 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=278619\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x+y=35_x=4y\r<BR>\n" );
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document.write( "Since y does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting y from both sides.<BR>\n" );
document.write( "x=-y+35_x=4y\r<BR>\n" );
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document.write( "Replace all occurrences of x with the solution found by solving the last equation for x.  In this case, the value substituted is -y+35.<BR>\n" );
document.write( "x=-y+35_(-y+35)=4y\r<BR>\n" );
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document.write( "Remove the parentheses around the expression -y+35.<BR>\n" );
document.write( "x=-y+35_-y+35=4y\r<BR>\n" );
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document.write( "Since 4y contains the variable to solve for, move it to the left-hand side of the equation by subtracting 4y from both sides.<BR>\n" );
document.write( "x=-y+35_-y+35-4y=0\r<BR>\n" );
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document.write( "Since -y and -4y are like terms, subtract 4y from -y to get -5y.<BR>\n" );
document.write( "x=-y+35_-5y+35=0\r<BR>\n" );
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document.write( "Since 35 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 35 from both sides.<BR>\n" );
document.write( "x=-y+35_-5y=-35\r<BR>\n" );
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document.write( "Divide each term in the equation by -5.<BR>\n" );
document.write( "x=-y+35_-(5y)/(-5)=-(35)/(-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( "x=-y+35_y=-(35)/(-5)\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( "x=-y+35_y=7\r<BR>\n" );
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document.write( "Replace all occurrences of y with the solution found by solving the last equation for y.  In this case, the value substituted is 7.<BR>\n" );
document.write( "x=-(7)+35_y=7\r<BR>\n" );
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document.write( "Multiply -1 by the 7 inside the parentheses.<BR>\n" );
document.write( "x=-7+35_y=7\r<BR>\n" );
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document.write( "Add 35 to -7 to get 28.<BR>\n" );
document.write( "x=28_y=7\r<BR>\n" );
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document.write( "This is the solution to the system of equations.<BR>\n" );
document.write( "x=28_y=7\r<BR>\n" );
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document.write( "x+y=43_x=5+y\r<BR>\n" );
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document.write( "Since y does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting y from both sides.<BR>\n" );
document.write( "x=-y+43_x=y+5\r<BR>\n" );
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document.write( "Replace all occurrences of x with the solution found by solving the last equation for x.  In this case, the value substituted is -y+43.<BR>\n" );
document.write( "x=-y+43_(-y+43)=y+5\r<BR>\n" );
document.write( "\n" );
document.write( "Remove the parentheses around the expression -y+43.<BR>\n" );
document.write( "x=-y+43_-y+43=y+5\r<BR>\n" );
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document.write( "Since y contains the variable to solve for, move it to the left-hand side of the equation by subtracting y from both sides.<BR>\n" );
document.write( "x=-y+43_-y+43-y=5\r<BR>\n" );
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document.write( "Since -y and -y are like terms, subtract y from -y to get -2y.<BR>\n" );
document.write( "x=-y+43_-2y+43=5\r<BR>\n" );
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document.write( "Since 43 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 43 from both sides.<BR>\n" );
document.write( "x=-y+43_-2y=-43+5\r<BR>\n" );
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document.write( "Add 5 to -43 to get -38.<BR>\n" );
document.write( "x=-y+43_-2y=-38\r<BR>\n" );
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document.write( "Divide each term in the equation by -2.<BR>\n" );
document.write( "x=-y+43_-(2y)/(-2)=-(38)/(-2)\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( "x=-y+43_y=-(38)/(-2)\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( "x=-y+43_y=19\r<BR>\n" );
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document.write( "Replace all occurrences of y with the solution found by solving the last equation for y.  In this case, the value substituted is 19.<BR>\n" );
document.write( "x=-(19)+43_y=19\r<BR>\n" );
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document.write( "Multiply -1 by the 19 inside the parentheses.<BR>\n" );
document.write( "x=-19+43_y=19\r<BR>\n" );
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document.write( "Add 43 to -19 to get 24.<BR>\n" );
document.write( "x=24_y=19\r<BR>\n" );
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document.write( "This is the solution to the system of equations.<BR>\n" );
document.write( "x=24_y=19\r<BR>\n" );
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document.write( "y=5x_y=2x+3\r<BR>\n" );
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document.write( "Replace all occurrences of y with the solution found by solving the last equation for y.  In this case, the value substituted is 5x.<BR>\n" );
document.write( "y=5x_(5x)=2x+3\r<BR>\n" );
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document.write( "Remove the parentheses around the expression 5x.<BR>\n" );
document.write( "y=5x_5x=2x+3\r<BR>\n" );
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document.write( "Since 2x contains the variable to solve for, move it to the left-hand side of the equation by subtracting 2x from both sides.<BR>\n" );
document.write( "y=5x_5x-2x=3\r<BR>\n" );
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document.write( "Since 5x and -2x are like terms, add -2x to 5x to get 3x.<BR>\n" );
document.write( "y=5x_3x=3\r<BR>\n" );
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document.write( "Divide each term in the equation by 3.<BR>\n" );
document.write( "y=5x_(3x)/(3)=(3)/(3)\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( "y=5x_x=(3)/(3)\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( "y=5x_x=1\r<BR>\n" );
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document.write( "Replace all occurrences of x with the solution found by solving the last equation for x.  In this case, the value substituted is 1.<BR>\n" );
document.write( "y=5(1)_x=1\r<BR>\n" );
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document.write( "Multiply 5 by each term inside the parentheses.<BR>\n" );
document.write( "y=5_x=1\r<BR>\n" );
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document.write( "This is the solution to the system of equations.<BR>\n" );
document.write( "y=5_x=1\r<BR>\n" );
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document.write( "x+y=39_x=y+5\r<BR>\n" );
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document.write( "Since y does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting y from both sides.<BR>\n" );
document.write( "x=-y+39_x=y+5\r<BR>\n" );
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document.write( "Replace all occurrences of x with the solution found by solving the last equation for x.  In this case, the value substituted is -y+39.<BR>\n" );
document.write( "x=-y+39_(-y+39)=y+5\r<BR>\n" );
document.write( "\n" );
document.write( "Remove the parentheses around the expression -y+39.<BR>\n" );
document.write( "x=-y+39_-y+39=y+5\r<BR>\n" );
document.write( "\n" );
document.write( "Since y contains the variable to solve for, move it to the left-hand side of the equation by subtracting y from both sides.<BR>\n" );
document.write( "x=-y+39_-y+39-y=5\r<BR>\n" );
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document.write( "Since -y and -y are like terms, subtract y from -y to get -2y.<BR>\n" );
document.write( "x=-y+39_-2y+39=5\r<BR>\n" );
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document.write( "Since 39 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 39 from both sides.<BR>\n" );
document.write( "x=-y+39_-2y=-39+5\r<BR>\n" );
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document.write( "Add 5 to -39 to get -34.<BR>\n" );
document.write( "x=-y+39_-2y=-34\r<BR>\n" );
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document.write( "Divide each term in the equation by -2.<BR>\n" );
document.write( "x=-y+39_-(2y)/(-2)=-(34)/(-2)\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( "x=-y+39_y=-(34)/(-2)\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( "x=-y+39_y=17\r<BR>\n" );
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document.write( "Replace all occurrences of y with the solution found by solving the last equation for y.  In this case, the value substituted is 17.<BR>\n" );
document.write( "x=-(17)+39_y=17\r<BR>\n" );
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document.write( "Multiply -1 by the 17 inside the parentheses.<BR>\n" );
document.write( "x=-17+39_y=17\r<BR>\n" );
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document.write( "Add 39 to -17 to get 22.<BR>\n" );
document.write( "x=22_y=17\r<BR>\n" );
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document.write( "This is the solution to the system of equations.<BR>\n" );
document.write( "x=22_y=17\r<BR>\n" );
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document.write( "x+y=328_x=y+12\r<BR>\n" );
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document.write( "Since y does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting y from both sides.<BR>\n" );
document.write( "x=-y+328_x=y+12\r<BR>\n" );
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document.write( "Replace all occurrences of x with the solution found by solving the last equation for x.  In this case, the value substituted is -y+328.<BR>\n" );
document.write( "x=-y+328_(-y+328)=y+12\r<BR>\n" );
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document.write( "Remove the parentheses around the expression -y+328.<BR>\n" );
document.write( "x=-y+328_-y+328=y+12\r<BR>\n" );
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document.write( "Since y contains the variable to solve for, move it to the left-hand side of the equation by subtracting y from both sides.<BR>\n" );
document.write( "x=-y+328_-y+328-y=12\r<BR>\n" );
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document.write( "Since -y and -y are like terms, subtract y from -y to get -2y.<BR>\n" );
document.write( "x=-y+328_-2y+328=12\r<BR>\n" );
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document.write( "Since 328 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 328 from both sides.<BR>\n" );
document.write( "x=-y+328_-2y=-328+12\r<BR>\n" );
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document.write( "Add 12 to -328 to get -316.<BR>\n" );
document.write( "x=-y+328_-2y=-316\r<BR>\n" );
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document.write( "Divide each term in the equation by -2.<BR>\n" );
document.write( "x=-y+328_-(2y)/(-2)=-(316)/(-2)\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( "x=-y+328_y=-(316)/(-2)\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( "x=-y+328_y=158\r<BR>\n" );
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document.write( "Replace all occurrences of y with the solution found by solving the last equation for y.  In this case, the value substituted is 158.<BR>\n" );
document.write( "x=-(158)+328_y=158\r<BR>\n" );
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document.write( "Multiply -1 by the 158 inside the parentheses.<BR>\n" );
document.write( "x=-158+328_y=158\r<BR>\n" );
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document.write( "Add 328 to -158 to get 170.<BR>\n" );
document.write( "x=170_y=158\r<BR>\n" );
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document.write( "This is the solution to the system of equations.<BR>\n" );
document.write( "x=170_y=158 </SPAN>\n" );
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