document.write( "Question 835353: The sum of two numbers is 25.their difference is 7.find the numbers.
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Algebra.Com's Answer #503475 by KMST(5328)\"\" \"About 
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USING JUST ONE VARIABLE:
\n" ); document.write( "\"x\"= the smaller number
\n" ); document.write( "\"x%2B7\"= the larger number (since the difference between them is 7)
\n" ); document.write( "\"x%2B%28x%2B7%29=25\" is our equation (because the sum of the two numbers is 25).
\n" ); document.write( "Solving:
\n" ); document.write( "\"x%2B%28x%2B7%29=25\"
\n" ); document.write( "\"%28x%2Bx%29%2B7=25\"
\n" ); document.write( "\"2x%2B7=25\"
\n" ); document.write( "\"2x=25-7\"
\n" ); document.write( "\"2x=18\"
\n" ); document.write( "\"x=18%2F2\"
\n" ); document.write( "\"highlight%28x=9%29\" is the smaller number.
\n" ); document.write( "Then, \"x%2B7=9%2B7=highlight%2816%29\" is the larger number.
\n" ); document.write( "The two numbers are \"highlight%289%29\" and \"highlight%2816%29\" .
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\n" ); document.write( "USING TWO VARIABLES:
\n" ); document.write( "\"x\"= the smaller number
\n" ); document.write( "\"y\"= the larger number
\n" ); document.write( "The equations are
\n" ); document.write( "\"x%2By=25\" (because the sum of the two numbers is 25), and
\n" ); document.write( "\"y-x=7\" (because the difference of the two numbers is 7).
\n" ); document.write( "We can solve the system \"system%28x%2By=25%2Cy-x=7%29\" by substitution by solving
\n" ); document.write( "\"y-x=7\" for \"y\" , getting \"y=x%2B7\" and then substituting \"x%2B7\" for \"y\" in \"x%2B4=25\" .
\n" ); document.write( "Then we get the one variable equation solved above.
\n" ); document.write( "We can also solve the system \"system%28x%2By=25%2Cy-x=7%29\" by graphing, or by the \"method\" that some call elimination. (Others call it combinations of equations.
\n" ); document.write( "For example, adding both equations, we get
\n" ); document.write( "\"y%2Bx=25\"
\n" ); document.write( "\"y-x=7\"
\n" ); document.write( "------------
\n" ); document.write( "\"y%2By=25%2B7\" --> \"2y=32\" --> \"y=32%2F2\" ---> h\"highligt%28y=16%29\"
\n" ); document.write( "Then we can substitute that value for \"y\" into either of the equations to find \"x\" , as in
\n" ); document.write( "\"x%2By=25\" --> \"x%2B16=25\" --> \"x=25-16\" --> \"highlight%28x=9%29\" .
\n" ); document.write( "To solve by graphing we graph the line that represents \"x%2By=25\" and the line that represents \"y-x=7\" . The coordinates of the point where they intersect is the (x,y) solution . We estimate it (read it) from the graph, to get the values of x and y that appear to be the solution, and then verify by plugging those values into the equations.
\n" ); document.write( "Graphing is a bit time consuming.
\n" ); document.write( "To graph one linear equation, we just need to points (or a pont and a slope).
\n" ); document.write( "For \"x%2By=25\" , we can see that (0,25) and {25,0) are two points in the graph, because when we set x to zero, the equation turns into \"y=25\" , and hen we set y to zero, the equation turns into \"x=25\" . The points (0,25) and (25,0) are the y-intercept and x-intercept, and we can use them to draw the line.
\n" ); document.write( "For \"y-x=7\" we can find the points (0,7) and (-7,0) in a similar way.
\n" ); document.write( " The intersection point coordinates appear to be \"x=9\" and \"y=16\" .
\n" ); document.write( "We verify by substituting into \"x%2By=25\" to get
\n" ); document.write( "\"x%2By=9%2B16=25\" .
\n" ); document.write( "We also need to verify that Those values make \"y=x=7\" true, so we calculate
\n" ); document.write( "\"y-x=16-9=7\".
\n" ); document.write( "With the values read from the graph verified, we can say that the solution found by graphing is
\n" ); document.write( "\"highlight%28system%28x=9%2Cy=16%29%29\" .
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