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3 years ago

Use elimination to solve the following system of equations: 17x - 2y = 25 17x + 3y = 5

Mathematics

1 answer:

Fynjy0 [20]3 years ago

6 0

Step-by-step explanation:

$17x - 2y = 25$

$17x + 3y = 5$

Both equations have a $17x$ term in them, so if we subtract the second equation from the first, it will eliminate those terms, allowing us to solve for the remaining $y$ terms:

$(17x - 2y) - (17x + 3y) = 25 - 5$

$(17x - 17x) + (-2y - 3y) = 20$

$-5y = 20$

$y = -4$

Finally, we can plug this value for $y$ into either of the two original equations to solve for $x$ :

$17x - 2(-4) = 25$

$17x + 8 = 25$

$17x = 17$

$x = 1$

This means the solution to the system of equations is $(1, -4)$ .

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Use the "rule of 72" to estimate the doubling time (in years) for the interest rate, and then calculate it exactly. (Round your

bonufazy [111]

Answer:

Using the rule of 72, the doubling time is 9.35 years.

The exact answer is that the doubling time is 8.89 years.

Step-by-step explanation:

By the rule of 72, we have that the doubling time D is given by:

$D = \frac{72}{Interest Rate}$

The interest rate is in %.

In our exercise, the interest rate is 7.7%. So, by the rule of 72:

$D = \frac{72}{7.7} = 9.35$ .

Exact answer:

The exact answer is going to be found using the compound interest formula(since the rule of 72 is a simplification of this formula).

The compound interest formula is given by:

$A = P(1 + \frac{r}{n})^{nt}$

Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

So, for this exercise, we have:

We want to find the doubling time, that is, the time in which the amount is double the initial amount, double the principal.

$A = 2P$