Solve the system of equations -x+y=15−x+y=15 and -5x-3y=27−5x−3y=27 by combining the equations

Mathematics

1 answer:

Genrish500 [490]2 years ago

8 0

Answer:

<em>Solution: x= -36, y=51</em>

Step-by-step explanation:

Solve the system:

x + y = 15

-5x - 3y = 27

By using the reduction method.

Multiply the first equation by 3:

3x + 3y = 45

Add it to the second equation:

3x - 5x = 45 + 27

Simplifying:

-2x = 72

Dividing by -2:

x = 72/(-2)

x = -36

From the first equation:

-36 + y = 15

Adding 36:

y = 15 + 36 = 51

y = 51

Solution: x= -36, y=51

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Type the correct answer in the box. Round your answer to the hundredth.

sesenic [268]

Answer:

Approximately 22.97 years

Step-by-step explanation:

Use the equation for continuously compounded interest, which uses the exponential base "e":

$A=P e^{k*t}$

Where P is the principal (initial amount of the deposit - unknown in our case)

A is the accrued value (value accumulated after interest is compounded), in our case it is not a given value but we know that it triples the original deposit (principal) so we write it as: 3 P (three times the principal)

k is the interest rate : 5% which translates into 0.05

and t is the time in the savings account to triple its value (what we need to find)

The formula becomes:

$3P = P e^{0.05 * t}$

To solve for "t" we divide both sides of the equation by P (notice it cancels P everywhere), and then to solve for the exponent "t" we use the natural logarithm function:

$\frac{3P}{P} = \frac{P}{P} e^{0.05 * t}$