document.write( "Question 74261: 1. Solve by elimination method
\n" ); document.write( "4x - y = -3
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\n" ); document.write( "\n" ); document.write( "2. Solve by graphing method
\n" ); document.write( "x - y = 3
\n" ); document.write( "x + y = 1\r
\n" ); document.write( "\n" ); document.write( "3. Solve by addition method
\n" ); document.write( "1/5x + 2/3y = -8/5
\n" ); document.write( "3x - y = 9 \n" ); document.write( "

Algebra.Com's Answer #53271 by rmromero(383) $\"\"$ $\"About$

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document.write( "1. Solve by elimination method 
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document.write( "4x - y = -3 
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document.write( "y - 3 = 4x \r
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document.write( "Rewrite the equation in standard form:
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document.write( "         4x - y = -3
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document.write( "         4x - y = -3
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document.write( "        _____________\r
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document.write( "         4x - y = -3
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document.write( "        -4x + y = +3
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document.write( "        _____________
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document.write( "          0 + 0 = 0\r
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document.write( "The equations are the same so there are many solution. 
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document.write( "The graph are same line
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document.write( "Let us look at the graph to check if there is a solution\r
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document.write( "2. Solve by graphing method
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document.write( "x - y = 3
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document.write( "x + y = 1 \r
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document.write( "To graph it easily, we will rewrite the equation in slope - intercept form
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document.write( "y = mx + b, where m = slope and b = y -intercept\r
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document.write( "x - y = 3 ------->        y =  x - 3  eq1, where m = 1 and b = -3
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document.write( "x + y = 1 ------->        y = -x + 1  eq2, where m = -1 and b = 1\r
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document.write( "To graph eq1 the first point is (0,-3). use the slope the locate second point
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document.write( "m=1 means move 1 unit up and 1 unit right. then draw a line\r
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document.write( "To graph eq2 the first point is (0,1). use the slope to locate the 2nd point
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document.write( "m=-1 means move 1 unit down and 1 unit right or 1 unit up and 1 unit left
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document.write( "then draw a line.
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document.write( "the graph looks like this:\r
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document.write( "Solution is (2, -1). the graph intersect when x = 2 and y = -1.\r
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document.write( "3. Solve by addition method
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document.write( "We use this method so that one variable will be eliminated.
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document.write( "           1/5x + 2/3y = -8/5      eq1
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document.write( "                3x - y = 9         eq2
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document.write( "Simplify eq1. Mutiply LCD -15 each term (eq1 only)
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document.write( "              3x + 10y = -24   eq1
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document.write( "              3x -   y =  9    eq2
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document.write( "             _______________\r
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document.write( "Notice, if we add the two equations, no variable will be eliminated\r
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document.write( "So we must multiply a certain number to do that
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document.write( "say we eliminate x,Multiply -1 eq2 
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document.write( "             
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document.write( "               3x + 10y = -24
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document.write( "            -1(3x -   y =  9)
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document.write( "             _______________\r
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document.write( "              3x + 10y = -24
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document.write( "             -3x +   y = -9
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document.write( "             _______________
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document.write( "               0 + 11y = -33  divide both sides by 11\r
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document.write( "                     y = -3\r
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document.write( "Substitute y = -3 to any of the equations
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document.write( "                 3x -   y =  9
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document.write( "                 3x -(-3) =  9
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document.write( "                   3x + 3 = 9    subtract 3 both sides
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document.write( "                       3x = 6    Divide 3 both sides
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document.write( "                        x = 2\r
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document.write( "Solution is (2,-3). The graph intersect when x = 2 and y = -3\r
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document.write( "Checking:\r
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