document.write( "Question 832250: Solve the simultenous equations; x-y=3 3y-3x=4 \n" ); document.write( "
Algebra.Com's Answer #501966 by math-vortex(648) $\"\"$ $\"About$
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document.write( "Hi, there--\r\n" );
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document.write( "THE PROBLEM:\r\n" );
document.write( "Solve the simultaneous equations:\r\n" );
document.write( "x - y = 3  \r\n" );
document.write( "3y - 3x = 4\r\n" );
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document.write( "A SOLUTION:\r\n" );
document.write( "Let's use the elimination method to solve this system of equations. Change the order of the x- and \r\n" );
document.write( "y-terms in the second equation so that both equation have x and y in the same order. I change the \r\n" );
document.write( "subtraction to an addition because addition is commutative and subtraction is not.\r\n" );
document.write( "3y - 3x = 4\r\n" );
document.write( "3y + (-3x) = 4\r\n" );
document.write( "-3x + 3y = 4\r\n" );
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document.write( "We want to add the equations together and eliminate one variable (In this case, the x-term.) Notice that \r\n" );
document.write( "the coefficient of the x-term in the second equation is -3. We need to multiply both sides of the first \r\n" );
document.write( "equation by the additive inverse of -3. That is 3.\r\n" );
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document.write( " x - y = 3  -----> 3x - 3y = 12\r\n" );
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document.write( "Now the x-terms will cancel out when we add the equations together.\r\n" );
document.write( "3x - 3y = 12\r\n" );
document.write( "-3x + 3y = 4\r\n" );
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document.write( "0 + 0 = 16\r\n" );
document.write( "0 = 16\r\n" );
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document.write( "When we see a situation like this, where both variables disappear, it means that the system of equations has no solution. \r\n" );
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document.write( "Let's look at the graph to see what's happening:\r\n" );
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document.write( "The green equation is x - y = 3. The red one is 3y - 3x = 4. \r\n" );
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document.write( "The solution to a system of simultaneous equations is the point or points they have in common. We see \r\n" );
document.write( "that these lines are parallel, so they will never intersect. Thus there is no solution to this system. The \r\n" );
document.write( "official math terminology is that this system is inconsistent.\r\n" );
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document.write( "Hope this helps! Feel free to email if you have any questions about the solution.\r\n" );
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document.write( "Good luck with your math,\r\n" );
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document.write( "Mrs. F\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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