document.write( "Question 1196067: Find the coordinates of the point where the line (x,y) = (3+2t, -1+3t) meets the line y=2x+5 .
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Algebra.Com's Answer #828754 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Find the coordinates of the point where the line (x,y) = (3+2t, -1+3t) meets the line y=2x+5 .
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document.write( "We want to find \"t\" such that\r\n" );
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document.write( "    x = 3 + 2t,\r\n" );
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document.write( "    y = -1 + 3t\r\n" );
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document.write( "For it, we substitute these expressions into equation y = 2x + 5.  It gives us\r\n" );
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document.write( "    -1 + 3t = 2*(3+2t) + 5.\r\n" );
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document.write( "Simplify and find \"t\"\r\n" );
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document.write( "    -1 + 3t = 6 + 4t + 5\r\n" );
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document.write( "    -1 - 6 - 5 = 4t - 3t\r\n" );
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document.write( "        -12    =   t.\r\n" );
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document.write( "Then the point's coordinates are  \r\n" );
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document.write( "    x = 3+2t = 3 + 2*(-12) = -21;  \r\n" );
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document.write( "    y = -1 + 3t = -1 + 3*(-12) = -37.\r\n" );
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document.write( "ANSWER.  The intersection point is (-21,-37).\r\n" );
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