document.write( "Question 582398: please help me to grasp the concept of solving with elimination method.
\n" ); document.write( "-3x+4y=1
\n" ); document.write( "-6+6y=-3\r
\n" ); document.write( "\n" ); document.write( "4x-8y=48
\n" ); document.write( "11x+3y=105.5\r
\n" ); document.write( "\n" ); document.write( "8x+11y=-50
\n" ); document.write( "-32x-44y=-200 \n" ); document.write( "

Algebra.Com's Answer #372204 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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solving with elimination method.
\n" ); document.write( "-3x + 4y = 1
\n" ); document.write( "-6x + 6y =-3
\n" ); document.write( "the idea is to multiply one or both equations so that one variable has the same coefficient, ideally one is positive and the other negative
\n" ); document.write( "Multiply the 1st equation by -2, add to the 2nd equation
\n" ); document.write( "+6x - 8y = -2
\n" ); document.write( "-6x + 6y = -3
\n" ); document.write( "----------------Adding eliminates x, find y
\n" ); document.write( "0 + -2y = -5
\n" ); document.write( "y = $\"%28-5%29%2F%28-2%29\"$
\n" ); document.write( "y = +2.5
\n" ); document.write( ";
\n" ); document.write( "find x using the 1st equation
\n" ); document.write( "-3x + 4(2.5) = 1
\n" ); document.write( "-3x + 10 = 1
\n" ); document.write( "-3x = 1 - 10
\n" ); document.write( "-3x = -9
\n" ); document.write( "divide both sides by -3
\n" ); document.write( "x = 3
\n" ); document.write( ":
\n" ); document.write( "Check our solution in the 2nd equation
\n" ); document.write( "-6x + 6y = -3
\n" ); document.write( "-6(3) + 6(2.5) = -3
\n" ); document.write( "-18 + 15 = -3
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( " 4x - 8y = 48
\n" ); document.write( "11x + 3y = 105.5
\n" ); document.write( "multiply the 1st equation by 3, the 2nd equation by 8
\n" ); document.write( "12x - 24y = 144
\n" ); document.write( "88x + 24y = 844
\n" ); document.write( "-----------------adding eliminates y, find x
\n" ); document.write( "100x + 0 = 988
\n" ); document.write( "x = 988/100
\n" ); document.write( "x = 9.88
\n" ); document.write( ":
\n" ); document.write( "Find y using the 1st equation
\n" ); document.write( "4(9.88) - 8y = 48
\n" ); document.write( "39.52 - 8y = 48
\n" ); document.write( "-8y = 48 - 39.52
\n" ); document.write( "-8y = 8.48
\n" ); document.write( "y = $\"8.48%2F%28-8%29\"$
\n" ); document.write( "y = -1.06
\n" ); document.write( ":
\n" ); document.write( "Check solution in the 2nd equation
\n" ); document.write( "11x + 3y = 105.5
\n" ); document.write( "11(9.88) + 3(-1.06) = 105.5
\n" ); document.write( "108.68 - 3.18 = 105.5
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( " 8x + 11y = -50
\n" ); document.write( "-32x -44y =-200
\n" ); document.write( "multiply the 1st equation by 4, add to the 2nd equation
\n" ); document.write( "+32x + 44y = -200
\n" ); document.write( "-32x -44y = -200
\n" ); document.write( "--------------
\n" ); document.write( "note that every term cancels, the two equations are equivalent, dependent \n" ); document.write( "

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