Algebra.Com's Answer #299114 by ankor@dixie-net.com(22740)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
I have 4 different problems that deal with Substitution Method & Addition Method in which I am hoping you will be able to help me understand how to solve them. \r
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document.write( "The first one is with Substitution Method   I can't figure out the solution sets.
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document.write( "Rearrange the 1st equation for substitution
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document.write( "y = (-x+1)
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document.write( "Replace y in the 2nd equation
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document.write( "x^2 + x(-x+1) - (-x+1)^2 = -11
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document.write( "x^2 - x^2 + x - (x^2 - 2x + 1) = -11
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document.write( "Combine like terms
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document.write( "x^2 - x^2 - x^2 + x + 2x - 1 + 11 = 0
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document.write( "-x^2 + 3x + 10 = 0
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document.write( "Change signs, multiply by -1
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document.write( "x^2 - 3x - 10 = 0
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document.write( "Factors to
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document.write( "(x-5)(x+2) = 0
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document.write( "Two solutions, find y for each of them using y = -x+1
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document.write( "x = 5, then y = -5 + 1 = -4
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document.write( "x = -2, then y = -(-2) + 1 = 3
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document.write( "The second one is with Substitution Method as well  
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document.write( "The 2nd equation will be used for substitution
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document.write( "x = (y-6)
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document.write( "Replace x in the 1st equation
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document.write( "(y-6)^2 + y^2 = 180
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document.write( "y^2 - 12y + 36 + y^2 = 180
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document.write( "Combine like terms
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document.write( "y^2 + y^2 - 12y + 36 - 180 = 0
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document.write( "2y^2 - 12y - 144 = 0
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document.write( "Simplify, divide by 2
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document.write( "y^2 - 6y - 72 = 0
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document.write( "Factors to
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document.write( "(y-12)(y+6) = 0
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document.write( "Two solutions
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document.write( "y = 12, then x = 12 - 6 = 6
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document.write( "y = -6, then x = -6 - 6 = -12
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document.write( "The third problem is with Addition Method  
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document.write( "Multiply the 1st equation by 7, multiply the 2nd equation by 3, we have
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document.write( "14x^2 + 21y^2 - 210 = 0
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document.write( "15x^2 - 21y^2 - 51 = 0
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document.write( "----------------------------Addition eliminates y^2, find x
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document.write( "29x^2 - 261 = 0
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document.write( "29x^2 = 261
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document.write( "x^2 = 
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document.write( "x^2 = 9
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document.write( "x = 3
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document.write( "Find y using the original 1st equation
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document.write( "2(3^2) + 3y^2 - 30 = 0
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document.write( "18 + 3y^2 - 30 = 0
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document.write( "3y^2 - 12 = 0
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document.write( "3y^2 = 12
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document.write( "y^2 = 
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document.write( "y^2 = 4
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document.write( "y = 2
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document.write( ":\r
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document.write( "The final problem is with addition method as well  
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document.write( "Multiply the 2nd equation by -1, arrange as follows
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document.write( "x^2 + y^2 = 16
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document.write( "0x^2 -y^2 + 3x = -16
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document.write( "-----------------------adding eliminates y^2 find x
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document.write( "x^2 + 3x = 0
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document.write( "Factor out x
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document.write( "x(x+3) = 0
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document.write( "Two solutions
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document.write( "x = 0
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document.write( "x = -3
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document.write( "Find y using the 1st equation
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document.write( "When x=0
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document.write( "0 + y^2 = 16
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document.write( "y = 4
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document.write( "When x=-3
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document.write( "-3^2 + y^2 = 16
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document.write( "y^2 = 16 - 9
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document.write( "y^2 = 7
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document.write( "y = 
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document.write( "You should check these solutions in the original equations, a lot of math here
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document.write( "mistakes are made, so check my work. \n" );
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