Solve the following simultaneous equations
(a)
(b) Given that y = axb + 10 and that y = 26 when x = 2 and y = 64
when x = 3, find the value of a and of b.
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Answer:
(a)
Substitute x = 3 + 2y into (2)
2(3 + 2y) + 3y = -1
6 + 4y + 3y = -1
7y = -7
y = -1
Substitute y = -1 into (1)
x = 3 + 2y
x = 3 + 2(-1)
x = 1
(b)
y = axb + 10
Substitute x = 2 and y = 26 into
y = axb + 10
26 = a(2)b + 10
16 = a(2)b ------------------ (1)
Substitute x = 3 and y = 64 into
y = axb + 10
64 = a(3)b + 10
54 = a(3)b ------------------ (2)
(2) / (1)
By comparison, b = 3
Substitute b = 3 into (1),
16 = a(2)3
16 = 8a
a = 2
