document.write( "Question 1071223: Solve the following pairs of simultaneous equations:\r
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\n" ); document.write( "\n" ); document.write( "Y=2×-1,Y=3x-2\r
\n" ); document.write( "\n" ); document.write( "2y=6x-4,Y=3x-2 \n" ); document.write( "
Algebra.Com's Answer #686144 by ikleyn(52787)\"\" \"About 
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\n" ); document.write( "Solve the following pairs of simultaneous equations:\r
\n" ); document.write( "\n" ); document.write( "X+2y=3,X-2y=3 \r
\n" ); document.write( "\n" ); document.write( "Y=2×-1,Y=3x-2\r
\n" ); document.write( "\n" ); document.write( "2y=6x-4,Y=3x-2
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document.write( "1. \r\n" );
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document.write( "x + 2y = 3,\r\n" );
document.write( "x - 2y = 3.\r\n" );
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document.write( "Add the two equations (both sides). The terms with \"y\" will cancel, and you will get\r\n" );
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document.write( "2x = 6, which implies x = 3.\r\n" );
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document.write( "Now, substitute the found value x= 3 into the first equation. You will get\r\n" );
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document.write( "3 + 2y = 3  --->  2y = 0  --->  y= 0.\r\n" );
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document.write( "Answer. The solution is x= 3, y= 0.\r\n" );
document.write( "        The method I applied is called the Elimination method.\r\n" );
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document.write( "2. \r\n" );
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document.write( "y = 2x - 1,\r\n" );
document.write( "y = 3x - 2.\r\n" );
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document.write( "Since the left sides are identical, the right sides are equal:\r\n" );
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document.write( "2x - 1 = 3x - 2  --->  -1 + 2 = 3x - 2x  --->  1 = x  --->  x = 1.\r\n" );
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document.write( "Now, substitute the found value x= 1 into the first equation. You will get\r\n" );
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document.write( "y = 2*1 - 1 = 2 - 1 = 1.\r\n" );
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document.write( "Answer.  The solution is x= 1, y= 1.\r\n" );
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document.write( "3.\r\n" );
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document.write( "2y = 6x - 4, \r\n" );
document.write( " y = 3x - 2.\r\n" );
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document.write( "In the first equation, divide both sides by 2. You will get an equivalent equation\r\n" );
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document.write( " y = 3x - 4.\r\n" );
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document.write( "Compare it with the second equation.\r\n" );
document.write( "You see that they are identical.\r\n" );
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document.write( "So, your system is actually one equation for two unknowns, since the second equation is equivalent to the first one.\r\n" );
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document.write( "Geometrically, these two equations represent one straight line.\r\n" );
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document.write( "The original system has infinitely many solutions.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On solving systems of two linear equations in two unknowns see the lessons \r
\n" ); document.write( "\n" ); document.write( "    - Solution of the linear system of two equations in two unknowns by the Substitution method \r
\n" ); document.write( "\n" ); document.write( "    - Solution of the linear system of two equations in two unknowns by the Elimination method \r
\n" ); document.write( "\n" ); document.write( "    - Solution of the linear system of two equations in two unknowns using determinant \r
\n" ); document.write( "\n" ); document.write( "    - Geometric interpretation of the linear system of two equations in two unknowns \r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Systems of two linear equations in two unknowns\".\r
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