please answer to these questions . the answer should be correct
Answers
b) Answer :
x = 3 , y = 2
Solution :
Here ,
The given equations are ;
(7 + x)/5 - (2x - y)/4 = 3y - 5 ---------(1)
(5y - 7)/2 + (4x - 3)/6 = 18 - 5x ---------(2)
Now ,
Eq-(1) can be rewritten as ;
=> (7 + x)/5 - (2x - y)/4 = 3y - 5
=> [4(7 + x) - 5(2x - y)]/20 = 3y - 5
=> 4(7 + x) - 5(2x - y) = 20(3y - 5)
=> 28 + 4x - 10x + 5y = 60y - 100
=> 10x - 4x + 60y - 5y - 100 - 28 = 0
=> 6x + 55y - 128 = 0 -------(3)
Now ,
Eq-(2) can be rewritten as ;
=> (5y - 7)/2 + (4x - 3)/6 = 18 - 5x
=> [3(5y - 7) + (4x - 3)]/6 = 18 - 5x
=> 3(5y - 7) + (4x - 3) = 6(18 - 5x)
=> 15y - 21 + 4x - 3 = 108 - 30x
=> 30x + 4x + 15y - 21 - 3 - 108 = 0
=> 34x + 15y - 132 = 0 -------(4)
Now ,
Multiplying eq-(3) by 17 , we get ;
=> 17(6x + 55y - 128) = 17•0
=> 102x + 935y - 2176 = 0 -------(5)
Now ,
Multiplying eq-(4) by 3 , we get ;
=> 3(34x + 15y - 132) = 3•0
=> 102x + 45y - 396 = 0 --------(6)
Now ,
Subtracting eq-(6) from (5) , we get ;
=> (102x+935y-2176) - (102x+45y-396) = 0
=> 102x +935y -2176 -102x -45y +396 = 0
=> 890y - 1780 = 0
=> 890y = 1780
=> y = 1780/890
=> y = 2
Now ,
Putting y = 2 in eq-(4) , we get ;
=> 34x + 15y - 132 = 0
=> 34x + 15•2 - 132 = 0
=> 34x + 30 - 132 = 0
=> 34x - 102 = 0
=> x = 102/34
=> x = 3
Hence ,
x = 3 , y = 2
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c) Answer :
9x² + 4y² - 12xy - 16
Solution :
- Given : (3x - 2y + 4)(3x - 2y - 4)
- To find : Expanded form of given expression .
We have ,
(3x - 2y + 4)(3x - 2y - 4)
The given express can be rewritten as ;
[(3x - 2y) + 4]•[(3x - 2y) - 4]
Clearly ,
The above expression is of the form
(A + B)(A - B) , where A = (3x - 2y) and B = 4
Now ,
Applying the formula (A + B)(A - B) = A² - B² for A = (3x - 2y) and B = 4 , we get ;
=> (3x - 2y + 4)(3x - 2y - 4)
= [(3x - 2y) + 4]•[(3x - 2y) - 4]
= (3x - 2y)² - 4²
=> (3x)² + (2y)² - 2•3x•2y - 4²
=> 9x² + 4y² - 12xy - 16
Hence ,
(3x - 2y + 4)(3x - 2y - 4) = 9x² + 4y² - 12xy - 16
Answer:
3rd page of math question paper
