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1 year ago

Answer the equation

Mathematics

1 answer:

ivanzaharov [21]1 year ago

4 0

Answer:

x = -2, y = -4

coordinate: (-2, -4)

Step-by-step explanation:

Given system of equations:

a) 4x - 7y = 20

b) x - 3y = 10

1. Make x the subject in the second equation:

⇒ x - 3y = 10 [add 3y to both sides]

⇒ x - 3y + 3y = 10 + 3y

⇒ x = 3y + 10

2. Substitute the given value of x into first equation:

⇒ 4x - 7y = 20

⇒ 4(3y + 10) - 7y = 20 [distribute 4 through the parentheses]

⇒12y + 40 - 7y = 20 [combine like terms]

⇒ 5y + 40 = 20 [subtract 40 from both sides]

⇒ 5y - 40 - 40 = 20 - 40

⇒ 5y = -20 [divide both sides by 5]

⇒ 5y ÷ 5 = -20 ÷ 5

⇒ y = -4

3. Find the value of x by substituting the given value of y into x = 3y + 10:

⇒ x = 3y + 10

⇒ x = 3(-4) + 10 [multiply]

⇒ x = -12 + 10 [add]

⇒ x = -2

4. Check your work:

a) 4x - 7y = 20

⇒ 4(-2) - 7(-4) = 20

⇒ -8 + 28 = 20

⇒ 20 = 20 ✔

b) x - 3y = 10

⇒ -2 - 3(-4) = 10

⇒ -2 + 12 = 10

⇒ 10 = 10 ✔

This system of equations has a solution at (-2, -4).

Learn more here:

brainly.com/question/27849342

brainly.com/question/27728118

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A person stands 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 meters

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Answer:

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Step-by-step explanation:

Given that,

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From Pythagorean Theorem,

(The distance between car and person)²= (The distance of the car from intersection)²+ (The distance of the person from intersection)²+

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Since the car driving towards the intersection at 13 m/s.

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$\therefore \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}.(-13)$

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