4x-3y=10 x+2y=-14 solve the equation using the linear combination method

Solve the system: 2/x - 3/y =-5; 4/x + 6\y =14

sertanlavr [38]

The solution is $x = 2 \text{ and } y = \frac{1}{2}$

Solution:

Let us assume,

$a = \frac{1}{x}\\\\b = \frac{1}{y}$

Given system of equations are:

$\frac{2}{x} - \frac{3}{y} = -5$

$\frac{4}{x} + \frac{6}{y} = 14$

Rewrite the equation using "a" and "b"

2a - 3b = -5 ------------ eqn 1

4a + 6b = 14 -------------- eqn 2

Let us solve eqn 1 and eqn 2

Multiply eqn 1 by 2

2(2a - 3b = -5)

4a - 6b = -10 ------------- eqn 3

Add eqn 2 and eqn 3

4a + 6b = 14

4a - 6b = -10

( - ) --------------------

8a = 4

$a = \frac{4}{8}\\\\a = \frac{1}{2}$

Substitute a = 1/2 in eqn 1

$2(\frac{1}{2}) -3b = -5\\\\1 - 3b = -5\\\\3b = 6\\\\b = 2$

Now let us go back to our assumed values

Substitute a = 1/2 in assumed values

$a = \frac{1}{x}\\\\\frac{1}{2} = \frac{1}{x}\\\\x = 2$

Substitute b = 2 in assumed value

$b = \frac{1}{y}\\\\2 = \frac{1}{y}\\\\y = \frac{1}{2}$

Thus the solution is $x = 2 \text{ and } y = \frac{1}{2}$

3 0

3 years ago

Venus Waldo reviewed her account statement and wanted to verify that the interest amount was correct. Her new balance was $12,09

user100 [1]

Answer:

The interest on the savings account is $46.47

Step-by-step explanation:

Here, we want to know the interest earned on the savings account.

The difference between the new and previous balance will be; 12,098.12 - 9,053.20 = $3,044.92

The difference between amount deposited and amount withdrawn is 3,298.45 - 300 = 2,998.45

This is the amount that is supposed to be on the account without interest

So the interest earned would be; 3044.92 - 2,998.45 = $46.47

3 0

3 years ago

What is the probability of getting either a sum of 5 or at least one 5 in the roll of a pair of dice?

maria [59]

In a throw of 2 fair dice, there are 6*6=36 equiprobability outcomes.

To get a sum of 5, there are 4 ways, (1,4),(2,3),(3,2),(4,1) with probability of 4/36=1/9

To get at least one 5, there are 6+6-1=11 outcomes (note (5,5) has been counted in both, so subtracted from sum). The probability is 11/36

Since the two events are mutually exclusive (once we have a five, the sum can no longer be 5), we can add the probabilities to get the probability of one event or the other.

P(sum of 5 OR at least one 5)=1/9+11/36=4/36+11/36=15/36=5/9

4 0

3 years ago

Look at the question below

ss7ja [257]

Answer:

y=6x is the answer

Step-by-step explanation:

6 0

3 years ago

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find the length of a segment indicated. Round your answer to the nearest tenth if necessary. NO LINKS.

Mademuasel [1]

9514 1404 393

Answer:

8. C) 24.2

9. A) 8.1

Step-by-step explanation:

8. The radius is shown as being 7.8 +4.3 = 12.1, so the diameter x is ...

d = 2r

x = 2(12.1) = 24.2

__

9. The unknown leg (y) of the right triangle can be found from the Pythagorean theorem.

y² +11.7² = 12.5² . . . . . the radius is half the diameter

y = √(156.25 -136.89) = √19.36 = 4.4

Then the segment of interest is ...

x + y = 12.5

x = 12.5 -4.4 = 8.1

6 0

3 years ago

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