document.write( "Question 118890: I HAVE NOW HAD PRACTICE SOLVING EQUATIONS WITH ONE VARIABLE AND EQUATIONS WITH TWO VARIABLES. Comparing equations with one variable to equations with two variables. How are they alike? How are they different? and what if an equation had three variables? \n" ); document.write( "

Algebra.Com's Answer #87117 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "the general rule for solving this kind of equations is:\r
\n" ); document.write( "\n" ); document.write( "if you have to find $\"one\"$ $\"+variable+\"$ you need $\"one\"$ $\"+equation\"$
\n" ); document.write( "if you have to find $\"two\"$ $\"+variables+\"$ you need $\"two\"$ $\"+equations\"$
\n" ); document.write( "if you have to find $\"three\"$ $\"+variables\"$ you need $\"three+equations\"$ \r
\n" ); document.write( "\n" ); document.write( ":and so on
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "if you have to find $\"n\"$ $\"+variables\"$ you need $\"n\"$ $\"+equations\"$
\n" ); document.write( " \r
\n" ); document.write( "\n" ); document.write( "If you compare of equations with $\"+one+\"$ and $\"two\"$ variables, they have similarities such as:\r
\n" ); document.write( "\n" ); document.write( "both of them have $\"an\"$ $\"+unknown\"$ number, which you need to get \r
\n" ); document.write( "\n" ); document.write( "in order to do it, you will need to use algebraic $\"formulas\"$ , $\"multiplication\"$ , $\"division\"$ , $\"addition\"$ , or $\"subtraction\"$ \r
\n" ); document.write( "\n" ); document.write( "The $\"difference\"$ between them is making $\"the+\"$ $\"ways\"$ in which they are treated to get the unknown number.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Many problems can be solved quickly and easily using $\"one+\"$ $\"equation\"$ with $\"one+\"$ $\"variable\"$ . \r
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\n" ); document.write( "\n" ); document.write( "Other problems that might be difficult to solve in terms of $\"one+\"$ $\"variable\"$ can easily be solved using $\"two\"$ $\"+equations\"$ and $\"two\"$ $\"+variables\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "the following example shows the difference in the $\"two\"$ $\"+methods\"$ ; solved first by using one variable and then using two:\r
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\n" ); document.write( "\n" ); document.write( "1. method\r
\n" ); document.write( "\n" ); document.write( " Find the two numbers such that half the first equals a third of the second and twice their sum exceeds three times the second by $\"4\"$ .\r
\n" ); document.write( "\n" ); document.write( " $\"x\"$ is first number\r
\n" ); document.write( "\n" ); document.write( "Then\r
\n" ); document.write( "\n" ); document.write( " $\"x%2F2=1%2F3\"$ of the second numberЕЕ=> $\"x=2%2F3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=2%2F3\"$ Е.multiply both sides by $\"3%2F2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%283%2F2%29x=%283%2F2%29%282%2F3%29\"$ Е.\r
\n" ); document.write( "\n" ); document.write( " $\"3x%2F2=1\"$ Е.\r
\n" ); document.write( "\n" ); document.write( " $\"3x%2F2\"$ Е.is second number\r
\n" ); document.write( "\n" ); document.write( "twice their sum exceeds three times the second by $\"4\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"2%28x++%2B+3x%2F2%29++=+3%283x%2F2%29+%2B+4+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2x++%2B+3x+=+9x%2F2+%2B+4+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"5x++=+9x%2F2+%2B+4+\"$ ЕЕЕmultiply both sides by $\"2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"10x++=+9x+%2B+8+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"10x+-++9x+=+8\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+8\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"8\"$ ЕЕЕЕЕis first number\r
\n" ); document.write( "\n" ); document.write( " $\"3x%2F2=3%2A8%2F2=3%2A4=12\"$ Е.\r
\n" ); document.write( "\n" ); document.write( " $\"12\"$ is second number\r
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\n" ); document.write( "\n" ); document.write( "2. method\r
\n" ); document.write( "\n" ); document.write( "If we let $\"x\"$ and $\"y\"$ be the first and second numbers, respectively, we can write $\"two\"$ equations:\r
\n" ); document.write( "\n" ); document.write( " $\"x%2F2=y%2F3\"$ ЕЕЕЕЕЕЕЕЕ.(1)\r
\n" ); document.write( "\n" ); document.write( " $\"2%28x%2By%29+=+3%2Ay+%2B+4\"$ ЕЕЕЕЕ.(2)\r
\n" ); document.write( "\n" ); document.write( "now solve for $\"x\"$ first equation, and substitute this value in the second:\r
\n" ); document.write( "\n" ); document.write( " $\"x%2F2=y%2F3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=2%28y%2F3%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+%282y%2F3%29+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2%282y%2F3+%2B+y%29+=+3y+%2B+4\"$ ЕЕЕЕЕ.(2)\r
\n" ); document.write( "\n" ); document.write( " $\"%284y%2F3%29+%2B2y+=+3y+%2B+4\"$ ЕЕЕЕЕmultiply both sides by $\"3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"4y+%2B+6y+=+9y+%2B+12\"$ ЕЕЕЕЕ\r
\n" ); document.write( "\n" ); document.write( " $\"+10y+=+9y+%2B+12\"$ ЕЕЕЕЕ\r
\n" ); document.write( "\n" ); document.write( " $\"+10y+-+9y+=+12\"$ ЕЕЕЕЕ\r
\n" ); document.write( "\n" ); document.write( " $\"+y+=+12\"$ ЕЕЕЕЕ\r
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( " $\"x+=2%28y%2F3%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=2%2812%2F3%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=2%284%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+8+\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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