document.write( "Question 450838: How do I solve the system by graphing x+y=21 and x-y=3? How do I figure out the point that lies on both lines? \n" ); document.write( "

Algebra.Com's Answer #310044 by Edwin McCravy(20056) $\"\"$ $\"About$

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How do I solve the system by graphing x+y=21 and x-y=3? How do I figure out the point that lies on both lines?
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document.write( "You have to be accurate with your drawings to get\r\n" );
document.write( "the answer by graphing.  Use graph paper and a ruler.\r\n" );
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document.write( "First we get some points on the line whose equation is \r\n" );
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document.write( "x + y = 21.\r\n" );
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document.write( "Just make up some arbitrary values for either of the \r\n" );
document.write( "letters x or y, substitute, and solve for the other \r\n" );
document.write( "letter.  This is my set of points.  You can pick \r\n" );
document.write( "different values from the ones I picked if you like.\r\n" );
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document.write( " x |  y\r\n" );
document.write( " 5 | 16   <---  I found that 16 this way:  x + y = 21\r\n" );
document.write( "10 | 11                                    5 + y = 21\r\n" );
document.write( " 0 | 21                                   -5       -5\r\n" );
document.write( "14 |  7                                   -----------\r\n" );
document.write( "                                               y = 16 \r\n" );
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document.write( "The others are found the same way.\r\n" );
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document.write( "Draw a line through them:\r\n" );
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document.write( "Then we get some arbitrary points on the line \r\n" );
document.write( "whose equation is \r\n" );
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document.write( "x - y = 3.  \r\n" );
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document.write( " x |  y\r\n" );
document.write( " 0 | -3\r\n" );
document.write( " 5 |  2\r\n" );
document.write( " 7 |  4\r\n" );
document.write( "14 | 11 \r\n" );
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document.write( "Draw a line through those points also:\r\n" );
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document.write( "Next draw a vertical line and a horizontal line\r\n" );
document.write( "through the point where those two lines cross.\r\n" );
document.write( "I'll draw them green:\r\n" );
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document.write( "Notice that one green line crosses the x-axis at 12, and\r\n" );
document.write( "notice that the other green line crosses the y-axis at 9.\r\n" );
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document.write( "Therefore the point where the two black lines intersect is\r\n" );
document.write( "the point (x,y) = (12,9).\r\n" );
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document.write( "Edwin

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