4x - 7y = 7
3x - 9y = 7
3(4x - 7y = 7)
12x - 21y = 21
-4(3x - 9y = 7)
-12x + 36y = -28
12x - 21y = 21
-12x + 36y = -28
15y = -7
y = -7/15
4x - 7(-7/15) = 7
4x + 49/15 = 7
4x = 7 - 49/15
4x = 105/15 - 49/15
4x = 56/15
x = (56/15) / (4)
x = (56/15) * (1/4)
x = 56/60 or 14/15
So the solution is x = 14/15 and y = -7/15 or (14/15, -7/15)
Verify solution by plugging in x and y values and solving.
Remark
This problem is done in 2 steps. The first step determines k and the second step is your answer.
Determining K
P = 233 million
A = 231 million
k = ??
t = 1999 - 1991 = 8 years.
Solution
P = Ae^(kt)
233 = 231 * e ^(kt) Divide by 231
233/231 = e^(k8) Do the division
1.008658 = e^(k8) Take the log of both sides.
ln(1.008658) = k8 * ln(e) You are in natural logs. Ln(e) = 1; kt can be brought down and made into a result that is multiplied by ln(e)
ln(1.008658) = 8k Take the ln of 1.008 ...
0.008621 = 8k Divide by 8
k = 0.008621 / 8
k = 0.0011 rounded, but a more accurate number is in the storage area of the calculator.
Now to get the second part.
P = ??
A = 231
k = 0.0011
t = 12
P = 231 * e^(0.0011*12)
P = 231 * e^(0.012931114) using the stored value of M
P = 231 * 1.013015083
P = 234.006 which rounded to the closest million is 234 million
Answer 234 million.
Answer:
The answer is D
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That's the only equation will get us one point