MATHEMATICS COLLEGE

Olve the system of equations below.3x+4y=10
6x-2y=40

(6,-2)

(2,6)

(2,-6)

(-2,-6)

Answers

Answer 1

Answer:

Answer:

The correct solutions are (6, -2).

Step-by-step explanation:

For the first equation, rearrange to make x the subject.

3x + 4y = 10

$3x = 10 -4y$

Divide the whole equation by 3 to isolate x:

$3x = 10 -4y\n3x / 3 = (10)/(3) - (4)/(3)y\nx = (10)/(3) - (4)/(3)y\n$

Now substitute this into the second equation:

$6x - 2y = 40\n6((10)/(3) - (4)/(3)y) - 2y = 40\n6((10)/(3)) + 6((4)/(3)) - 2y = 40$

$20 - 8y - 2y = 40\n20 - 10y = 40$

Subtract 20 from both sides:

20 - 10y = 40

20 - 10y - 20 = 40 - 20

-10y = 20

Divide both sides by 2:

-10y ÷ 10 = 20 ÷ 10

-y = 2 ∴ y = -2

Plug this value back into the first equation:

3x + 4y = 10

3x + 4(-2) = 10

3x + (-8) = 10

3x - 8 = 10

Add 8 to both sides:

3x - 8 + 8 = 10 + 8

3x = 18

Divide both sides by 3:

3x ÷ 3 = 18 ÷ 3

x = 6

Therefore, the correct solutions are (6, -2).

Hope this helps!

Related Questions

Interpret the regression coefficients. Fill in the blanks below. The [a. coefficient of determination b. correlation coefficient intercept slope coefficient] is the estimated amount of a purchase if time spent viewing the online catalog were zero. The a. intercept b. coefficient of determination c. slope coefficient d. correlation coefficient] is the estimate of amount that a purchase changes for one extra minute spent viewing the online catalog. b. Compute the coefficient of determination and interpret its meaning. Fill in the blanks below. The [a. proportion b. amount] of the total variation in purchases that can be explained by variation in the minutes spent viewing the? on-line catalog is equal to the coefficient of? determination, which is ____. (Round to three decimal places as needed) State the conclusion. Fill in the blanks below. [a. Do not Reject b. Reject] the null hypothesis. There is [a. sufficient b. insufficient] evidence to support the claim that the overall model is significant. The p-value is ____. (Round to three decimal places as needed.) State the conclusion. Fill in the blanks below. a.Do not Reject b. Reject c. the null hypothesis. There is a. sufficient b. insufficient evidence to support the claim that the overall model is significant. Determine the p-value. The p-value is ____. (Round to three decimal places as needed.) State the conclusion. Fill in the blanks below. [a. Reject b. Do not Reject] the null hypothesis. There is [a. insufficient b. sufficient] evidence to support the claim that the regression slope coefficient is not equal to zero.
10x² - 43x+28How do you factor this
I need some help with this
B) How many prime numbers are multiplesof 8?
Need help with 5. Part C

What is the value of x in both a & b?

Answers

Answer:

a. x=9, b. x=6

Step-by-step explanation:

In a the triangle is cut in half. the sides are equal even though the triangle is slanted.

In b the triangles are similar if you flip the big one. Since the smaller triangle is smaller it is a reduced form of the larger one.

Course hero; suppose you are assigned the number 1, and the other students in your statistics class call out consecutive numbers until each person in the class has his or her own number. (a) explain how you could get a random sample of four students from your statistics class.

Answers

Use the free service at Random.Org to generate a true random sample from the number of persons in your class. The attachment shows a random sample from the range 1–35. Use the numbers generated to select persons from the class with the same indentifying number.

Two less than three-fourths of a number is, at most, negative seventeen. what is the range of values for the number?

Answers

Answer:

$x\leq -20$

values ranging fromminus infinity to negative 20

Step-by-step explanation:

we write the inequality associated with the text in terms of the unknown number "x" as:

$(3)/(4) x-2\leq -17$

then, we solve for "x" by adding 2 to both sides, and then isolating "x" on the left as shown below:

$(3)/(4) x-2\leq -17\n(3)/(4) x\leq -17+2\n(3)/(4) x\leq -15\n3\,x\leq -60\nx\leq -(60)/(3) \nx\leq -20$

then, the range of x-values is from minus infinity to negative 20

Weights of men: 90% confidence; n = 14, x=161.5 lb, s =13.7 lb

Answers

Answer:

The 90% for the average weights of men is between 137.24 lb and 185.76 lb.

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 14 - 1 = 14

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of $1 - (1 - 0.9)/(2) = 0.95$ . So we have T = 1.7709