Suppose
a+4b+9c+16d+25e=-13,
4a+9b+16c +25d +36e =-8,
9a+16b+25c+36d+49e=3,
Find the value of
16a+25b+36c+49d+64e=?
Are you sure your third equation is not
9a+ 16b+ 25c +36d +49e = -3 ?
Then it would fall into a certain pattern with the others.
16a +25b +36c +49d +64e = +2
In general, your first three equations in five unknowns have an infinite number of possible solutions, so that the fourth equation cannot be solved uniquely
price of a home is 164,000. bank requires a 20% down payment and 3 points at closing. the cost of the home is financed with a 30 year fixed rate mortgage at 9%
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To find the value of 16a + 25b + 36c + 49d + 64e, we can start by manipulating the given equations to simplify them.
Let's label these equations as follows:
Equation 1: a + 4b + 9c + 16d + 25e = -13
Equation 2: 4a + 9b + 16c + 25d + 36e = -8
Equation 3: 9a + 16b + 25c + 36d + 49e = 3
Now, let's multiply each equation by a specific number and then sum them up in a way that will eliminate some of the variables. This method is known as "elimination."
Multiplying Equation 1 by 4, Equation 2 by -1, and Equation 3 by 1, we get:
4a + 16b + 36c + 64d + 100e = -52
-4a - 9b - 16c - 25d - 36e = 8
9a + 16b + 25c + 36d + 49e = 3
Now, let's sum up those equations:
4a - 4a + 16b + 16b + 36c - 16c + 64d - 25d + 100e - 36e = -52 + 8 + 3
32b + 20d + 64e = -41
Next, we can simplify the equation we obtained by dividing both sides by 4:
8b + 5d + 16e = -41/4
Now, let's rearrange this equation:
16e = -41/4 - 8b - 5d
16e = (-41 - 32b - 20d)/4
16e = (-41 - 32b - 20d)/4
Therefore, the value of 16a + 25b + 36c + 49d + 64e is given by substituting the value of 16e we just calculated into Equation 3:
16a + 25b + 36c + 49d + 64e = 16a + 25b + 36c + 49d + 64(-41 - 32b - 20d)/4
Now, simplifying this equation will give us the final answer.