document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=967820>Question 967820</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Stuck on how to solve this simultaneous equation \r<BR>\n" );
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document.write( "X^2+y^2=25<BR>\n" );
document.write( "X+y=7\r<BR>\n" );
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document.write( "ASAP please\r<BR>\n" );
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document.write( "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 #591552 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=591552\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have 2 equations.<BR>\n" );
document.write( "they are:\r<BR>\n" );
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document.write( "x^2 + y^2 = 25<BR>\n" );
document.write( "x + y = 7\r<BR>\n" );
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document.write( "solve for y in the second equation to get y = 7 - x<BR>\n" );
document.write( "replace y in the first equation to get x^2 + (7-x)^2 = 25\r<BR>\n" );
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document.write( "now that your first equation is in terms of x only, you can solve for x.<BR>\n" );
document.write( "once you solve for x, then use that value to solve for y.\r<BR>\n" );
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document.write( "start with x^2 + (7-x)^2 = 25<BR>\n" );
document.write( "simplify to get x^2 + 49 - 14x + x^2 = 25<BR>\n" );
document.write( "combine like terms to get 2x^2 - 14x + 49 = 25<BR>\n" );
document.write( "subttract 25 from both sides of the equation to get 2x^2 - 14x + 24 = 0<BR>\n" );
document.write( "divide both sides of the equation by 2 to get x^2 - 7x + 12 = 0<BR>\n" );
document.write( "factor that quadratic equation to get (x - 4) * (x - 3) = 0<BR>\n" );
document.write( "solve for x to get x = 4 or x = 3.\r<BR>\n" );
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document.write( "go back to the second original equation and solve for y using those values of x.<BR>\n" );
document.write( "when x = 3, y = 4<BR>\n" );
document.write( "when x = 4, y = 3\r<BR>\n" );
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document.write( "you have two possible pairs of solutions:\r<BR>\n" );
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document.write( "(x,y) = (4,3)<BR>\n" );
document.write( "(x,y) = (3,4)\r<BR>\n" );
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document.write( "go back to both original equations and see if these solutions make those equation true.\r<BR>\n" );
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document.write( "both original equations are:\r<BR>\n" );
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document.write( "x^2 + y^2 = 25<BR>\n" );
document.write( "x + y = 7\r<BR>\n" );
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document.write( "when x = 3 and y = 4, the equations become:\r<BR>\n" );
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document.write( "3^2 + 4^2 = 25 which becomes 9 + 16 = 24 which becomes 25 = 25 which is true.<BR>\n" );
document.write( "3 + 4 = 7 which becomes 7 = 7 which is true.\r<BR>\n" );
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document.write( "when x = 4 and y = 3, the equations becomes:\r<BR>\n" );
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document.write( "4^2 + 3^2 = 25 which becomes 25 = 25 which is true.<BR>\n" );
document.write( "4 + 3 = 7 which becomes 7 = 7 which is true.\r<BR>\n" );
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document.write( "looks like those are your solutions.\r<BR>\n" );
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document.write( "the graph of both equations is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C-1%2C6%2C-1%2C6%2C7-x%2Csqrt%2825-x%5E2%29%2C-sqrt%2825-x%5E2%29%2C90%28x-3%29%2C90%28x-4%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the 2 vertical lines at x = 3 and x = 4 show where the intersection of the graph of the two equations is.\r<BR>\n" );
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