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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.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Use elimination to solve:
x/3 + 4y = 30
2x - y = 5
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Multiply the 1st equation by 6 to get rid of the denominator, and
giving us a 2x to use for easy elimination, results:
2x + 24y = 180
2x - y = 5
----------------subtracting eliminates x, find y;
0x + 25y = 175
25y = 175
y = 175/25
y = 7
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Find x using 2x - y = 5
2x - 7 = 5
2x = 5 + 7
2x = 12
x = 12/2
x = 6
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Check solutions using 1st equation
6/3 + 4(7) =
2 + 28 = 30; confirms our solution
:
:
Use elimination to solve:
6x - y/4 = -9
3x + 2y = -30.
:
Multiply 1st equation by 8, eliminates the fraction and
gives a 2y for easy elimination:
48x - 2y = -72
3x + 2y = -30
----------------adding eliminates y, find x
51x + 0y = -102
51x = -102
x = -102/51
x = -2
:
Find y, using 3x + 2y = -30
3(-2) + 2y = -30
-6 + 2y = -30 + 6
2y = -24
y = -24/2
y = -12
:
Check solution in 1st equation:
6(-2) - (-12/4) =
-12 + 3 = -9
:
:
Solve the system of equations by substitution:
y = x^2 + 2x - 2
y = 3x + 4
:
Substitute (3x+4) for y in the 1st equation:
x^2 + 2x - 2 = 3x + 4
x^2 + 4x - 3x - 2 - 4 = 0
x^2 + x - 6 = 0; a quadratic equation:
Factor:
(x-3)(x+2) = 0
x = +3 and x = -2
Find y using the 2nd equation, when x = +3
y = 3(3) + 4
y = 13
when x = -2
y = 3(-2) + 4
y = -2
:
You can check both solutions by substituting for x in the 1st equation:
:
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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?
:
Let a = lbs of apple, and p = lbs of pears
The total lb equation:
a + p = 8
or
p = (8 - a); use for substitution:
:
The total cost equation:
1.50a + 2.30p = 14.00
Substitute (8-a) for p in the above equation:
1.5a + 2.3(8-a) = 14
1.5a + 18.4 - 2.3a = 14
1.5a - 2.3a = 14 - 18.4
-.8a = -4.4
a = -4.4/-.8
a = + 5.5 lb of apples
Find p using the lb equation:
p = 8 - 5.5
p = 2.5 lb of pears
:
Check solution in the cost equation:
1.5(5.5) + 2.3(2.5) =
8.25 + 5.75 = 14; confirms our solutions
:
How about this, are you understanding what's going on here?
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