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schepotkina [342]
2 years ago
8

Define a substitution method to solve the followingsysten of equation of y=2x-3, x+y=1

Mathematics
1 answer:
Ivan2 years ago
7 0
I will solve you system by substitution

y = 2x - 3 ; x + y = 1

→Step 1: Solve y = 2x - 3 for y

→Step 2: Substitute 2x - 3 for y in x + y = 1:

x + y = 1 

x + 2x- 3 = 1

3x - 3 = 1 (Simplify both sides of the equation)

3x - 3  + 3 = 1 + 3 (Add 3 both sides)

3x = 4 
 
3x ÷ 3 = 4 ÷ 3 (Divide each side by 3)

x = 4/3

→Step 3: Substitute 4/3 for x in y = 2x - 3:  

y = 2x - 3 

y = 2 (4/3) -3 

y = -1/3 (Simplify both sides of the equation)

Answer: 

x = 4/3 and y = -1/3

∫Hope that helps∫
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You own a motel and have a pricing structure that encourages rentals of rooms in groups.
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Answer:

$41

Step-by-step explanation:

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So,

a_1=\$68\\ \\a_2=\$65\\ \\a_3=\$62\\ \\...

where a_n is the rate per nth room rented.

This is an arithmetic sequence, so

a_n=a_1+(n-1)\cdot d

In your case,

a_1=68\\ \\n=10\\ \\d=-3

Hence

a_{10}=68+(10-1)\cdot (-3)=68-9\cdot 3=68-27=41

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3 years ago
Faucet A flows at a rate of 100 liters per 5 minutes and Faucet B flows at a rate of 100 liters per 4 minutes into an empty pool
Dmitriy789 [7]

Answer:

It will take both faucets 200 minutes to fill a pool with 9,000 liters of water

Step-by-step explanation:

Here, we want to know the time it will take for both faucets to fill a pool with 9,000 liters of water

What we need here is to have a joint rate for both faucets;

For the first faucet, we have a rate of 100 liters per 5 minutes so this means in a minute;

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For the second faucet, the per minute rate will be 100/4 = 25 liters per minute

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So the time needed to fill 9,000 liters of water in a pool will be ;

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