2.a.(i) Solve the simultaneous equations:
2x +3y =13
3x - y=3
(ii)Using the reault of (a)(i),solve the simultaneous equations:
2(a+b)+3(a-b)=13
3(a+b)-(a-b)=3
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simultaneous linear equations in two unknowns (f.2)
2007-03-06 7:45 am
回答 (2)
2007-03-06 9:07 pm
2007-03-06 8:01 am
(i)
2x + 3y = 13 -- (1)
3x - y = 3 -- (2)
(2) * 3 : 9x - 3y = 9 -- (2')
(1) + (2') : (2x + 3y) + (9x - 3y) = 13 + 9
11x = 22
x = 2
Sub x = 2 into (2)
3(2) - y = 3
y = 3(2) - 3
= 3
So, x = 2 and y = 3
(ii)
By comparison, a + b = x and a - b = y.
a + b = 2 -- (1)
a - b = 3 -- (2)
(1) + (2) : 2a = 5
a = 5/2
(1) - (2) : 2b = -1
b = -1/2
So, a = 5/2 and b = -1/2.
2x + 3y = 13 -- (1)
3x - y = 3 -- (2)
(2) * 3 : 9x - 3y = 9 -- (2')
(1) + (2') : (2x + 3y) + (9x - 3y) = 13 + 9
11x = 22
x = 2
Sub x = 2 into (2)
3(2) - y = 3
y = 3(2) - 3
= 3
So, x = 2 and y = 3
(ii)
By comparison, a + b = x and a - b = y.
a + b = 2 -- (1)
a - b = 3 -- (2)
(1) + (2) : 2a = 5
a = 5/2
(1) - (2) : 2b = -1
b = -1/2
So, a = 5/2 and b = -1/2.
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