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3 years ago

2y=-x+93×-6y=-15 whats the solution to the system

Mathematics

2 answers:

liq [111]3 years ago

8 0

Answer:

Step-by-step explanation:

2y = -x +9

3x - 6y = -15

The solution is the value of x and y that will make the two equations true in the same time.

3x-6y = -15; divide both sides by 3

x-2y = -5; substitute 2y for -x+9 because the first equation tell us they are equal

x-(-x+9) = -5; open parenthesis

x+x-9 = -5 ; add 9 to both sides and combine like terms

2x = -5 +9; 2x = 4; divide both sides by 2

x= 2

Substitute x for 2

2y = -x+9 ; 2y = -2 +9 ; 2y = 7; y = 7/2 = 3.5

Solution is (2, 3.5)

astraxan [27]3 years ago

3 0

Answer:

(2, 7/2)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtract Property of Equality

Algebra I

Coordinates (x, y)
Terms/Coefficients
Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

2y = -x + 9

3x - 6y = -15

Step 2: Rewrite Systems

2y = -x + 9

[Division Property of Equality] Divide 2 on both sides: y = -x/2 + 9/2

Step 3: Redefine Systems

y = -x/2 + 9/2

3x - 6y = -15

Step 4: Solve for x

Substitute in y: 3x - 6(-x/2 + 9/2) = -15
Distribute -6: 3x + 3x - 27 = -15
Combine like terms: 6x - 27 = -15
[Addition Property of Equality] Add 27 on both sides: 6x = 12
[Division Property of Equality] Divide 6 on both sides: x = 2

Step 5: Solve for y

Define original equation: 2y = -x + 9
Substitute in x: 2y = -2 + 9
Add: 2y = 7
[Division Property of Equality] Divide 2 on both sides: y = 7/2

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Answer:

a) The p-value of the test is 0.0076 < 0.05, which means that there is evidence of a difference between males and females in the proportion who said they prefer window tinting as a luxury upgrade at the 0.05.

b) The null hypothesis is $H_0: \pi_1 - \pi_2 = 0$ and the alternate hypothesis is $H_1: \pi_1 - \pi_2 \neq 0$ .

Step-by-step explanation:

Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

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49% from a sample of 600. So

$\pi_1 = 0.49, s_{\pi_1} = \sqrt{\frac{0.49*0.51}{600}} = 0.0204$

Males:

41% from a sample of 500. So

$\pi_2 = 0.41, s_{\pi_2} = \sqrt{\frac{0.41*0.59}{500}} = 0.022$

Test if there is a difference between males and females in the proportion who said they prefer window tinting as a luxury upgrade.

From here, question b can already be answered.

At the null hypothesis we test if there is no difference, that is, the subtraction of the proportions is 0. So

$H_0: \pi_1 - \pi_2 = 0$

At the alternate hypothesis, we test if there is a difference, that is, the subtraction of the proportions is different of 0. So

$H_1: \pi_1 - \pi_2 \neq 0$

The test statistic is:

$z = \frac{X - \mu}{s}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that $\mu = 0$

From the two samples:

$X = \pi_1 - \pi_2 = 0.49 - 0.41 = 0.08$

$s = \sqrt{s_{\pi_1}^2 + s_{\pi_2}^2} = \sqrt{0.0204^2 + 0.022^2} = 0.03$

Value of the test statistic:

$z = \frac{X - \mu}{s}$

$z = \frac{0.08 - 0}{0.03}$

$z = 2.67$

Question a:

P-value of the test and decision:

The p-value of the test is the probability that the sample proportion differs from 0 by at least 0.08, which is P(|Z| > 2.670, which is 2 multiplied by the p-value of Z = -2.67.

Looking at the z-table, Z = -2.67 has a p-value of 0.0038.

2*0.0038 = 0.0076

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3 years ago

2y=-x+93×-6y=-15 whats the solution to the system​

2y=-x+93×-6y=-15 whats the solution to the system