document.write( "Question 103868: Hello out there,I need some help with some tough problems,the first one is,Use elimination to solve:x/3+4y=30 and 2x-y=5.The next one is,Use elimination to solve:6x-y/4=-9 and 3x+2y=-30.The third one is,Solve the system of equations by substitution:y=x^2+2x-2 and y=3x+4.The last one is,Mr.Adams buys a bag of apples and a bag of pears for a total of $14.00.There are eight pounds of fruit in all.The apples cost $1.50 per pound,and the pears cost $2.30 per pound.How many pounds of pears did he buy?Thanks to whoever can help. \n" ); document.write( "
Algebra.Com's Answer #75756 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
Use elimination to solve:
\n" ); document.write( "x/3 + 4y = 30
\n" ); document.write( " 2x - y = 5
\n" ); document.write( ":
\n" ); document.write( "Multiply the 1st equation by 6 to get rid of the denominator, and
\n" ); document.write( "giving us a 2x to use for easy elimination, results:
\n" ); document.write( "2x + 24y = 180
\n" ); document.write( "2x - y = 5
\n" ); document.write( "----------------subtracting eliminates x, find y;
\n" ); document.write( "0x + 25y = 175
\n" ); document.write( "25y = 175
\n" ); document.write( "y = 175/25
\n" ); document.write( "y = 7
\n" ); document.write( ":
\n" ); document.write( "Find x using 2x - y = 5
\n" ); document.write( "2x - 7 = 5
\n" ); document.write( "2x = 5 + 7
\n" ); document.write( "2x = 12
\n" ); document.write( "x = 12/2
\n" ); document.write( "x = 6
\n" ); document.write( ":
\n" ); document.write( "Check solutions using 1st equation
\n" ); document.write( "6/3 + 4(7) =
\n" ); document.write( "2 + 28 = 30; confirms our solution
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Use elimination to solve:
\n" ); document.write( "6x - y/4 = -9
\n" ); document.write( "3x + 2y = -30.
\n" ); document.write( ":
\n" ); document.write( "Multiply 1st equation by 8, eliminates the fraction and
\n" ); document.write( "gives a 2y for easy elimination:
\n" ); document.write( "48x - 2y = -72
\n" ); document.write( " 3x + 2y = -30
\n" ); document.write( "----------------adding eliminates y, find x
\n" ); document.write( "51x + 0y = -102
\n" ); document.write( "51x = -102
\n" ); document.write( "x = -102/51
\n" ); document.write( "x = -2
\n" ); document.write( ":
\n" ); document.write( "Find y, using 3x + 2y = -30
\n" ); document.write( "3(-2) + 2y = -30
\n" ); document.write( "-6 + 2y = -30 + 6
\n" ); document.write( "2y = -24
\n" ); document.write( "y = -24/2
\n" ); document.write( "y = -12
\n" ); document.write( ":
\n" ); document.write( "Check solution in 1st equation:
\n" ); document.write( "6(-2) - (-12/4) =
\n" ); document.write( "-12 + 3 = -9
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Solve the system of equations by substitution:
\n" ); document.write( "y = x^2 + 2x - 2
\n" ); document.write( "y = 3x + 4
\n" ); document.write( ":
\n" ); document.write( "Substitute (3x+4) for y in the 1st equation:
\n" ); document.write( "x^2 + 2x - 2 = 3x + 4
\n" ); document.write( "x^2 + 4x - 3x - 2 - 4 = 0
\n" ); document.write( "x^2 + x - 6 = 0; a quadratic equation:
\n" ); document.write( "Factor:
\n" ); document.write( "(x-3)(x+2) = 0
\n" ); document.write( "x = +3 and x = -2
\n" ); document.write( "Find y using the 2nd equation, when x = +3
\n" ); document.write( "y = 3(3) + 4
\n" ); document.write( "y = 13
\n" ); document.write( "when x = -2
\n" ); document.write( "y = 3(-2) + 4
\n" ); document.write( "y = -2
\n" ); document.write( ":
\n" ); document.write( "You can check both solutions by substituting for x in the 1st equation:
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Mr.Adams buys a bag of apples and a bag of pears for a total of $14.00.There are eight pounds of fruit in all.The apples cost $1.50 per pound,and the pears cost $2.30 per pound.How many pounds of pears did he buy?
\n" ); document.write( ":
\n" ); document.write( "Let a = lbs of apple, and p = lbs of pears
\n" ); document.write( "The total lb equation:
\n" ); document.write( "a + p = 8
\n" ); document.write( "or
\n" ); document.write( "p = (8 - a); use for substitution:
\n" ); document.write( ":
\n" ); document.write( "The total cost equation:
\n" ); document.write( "1.50a + 2.30p = 14.00
\n" ); document.write( "Substitute (8-a) for p in the above equation:
\n" ); document.write( "1.5a + 2.3(8-a) = 14
\n" ); document.write( "1.5a + 18.4 - 2.3a = 14
\n" ); document.write( "1.5a - 2.3a = 14 - 18.4
\n" ); document.write( "-.8a = -4.4
\n" ); document.write( "a = -4.4/-.8
\n" ); document.write( "a = + 5.5 lb of apples
\n" ); document.write( "Find p using the lb equation:
\n" ); document.write( "p = 8 - 5.5
\n" ); document.write( "p = 2.5 lb of pears
\n" ); document.write( ":
\n" ); document.write( "Check solution in the cost equation:
\n" ); document.write( "1.5(5.5) + 2.3(2.5) =
\n" ); document.write( "8.25 + 5.75 = 14; confirms our solutions
\n" ); document.write( ":
\n" ); document.write( "How about this, are you understanding what's going on here?
\n" ); document.write( ":
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