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2 years ago

Solve the system with elimination. {2x-y=2, -5x+4y=-2

Mathematics

1 answer:

DaniilM [7]2 years ago

6 0

Answer:

{x=2,y=2

Step-by-step explanation:

Equation 1:

Multiply both sides of the equation by a coefficient

{ 4(2x-y)=2*4

-5x+4y=-2

Apply Multiplicative Distribution Law

{8x-4y=2*4,-5x+4y=-2

8x-4y+(-5x+4y)=8+(-2)

Remove parentheses

8x-4y-5x+4y=8-2

Cancel one variable

8x-5x=8-2

Combine like terms

3x=8-2

Calculate the sum or difference

3x=6

Divide both sides of the equation by the coefficient of the variable

x=6/3

Calculate the product or quotient

x=2

Equation two:

{-5+4y=-2, x=2

-5*2+4y=-2

Calculate the product or quotient

-10+4y =-2

Reduce the greatest common factor (GCF) on both sides of the equation

-5+2y=-1

Rearrange unknown terms to the left side of the equation

2y=-1+5

Calculate the sum or difference

2y=4

Divide both sides of the equation by the coefficient of the variable

y=4/2

y=2

Hope this helps!!

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Suppose the average yearly salary of an individual whose final degree is a master's is $45 thousand less than twice that of an

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Answer:

Step-by-step explanation:

let the degree holder earn x

then a masters degree holder earns= (2x-45,000)

the comnined amount of the two degree holders= (2x-45,000)+x

2x-45000+x=117000

3x=117000+45000

3x=162000

x=162000/3

x=$54000

so bachelor'sdegree hold earns= $54000

a masters degree holder earns= (2(54000)-45,000)

a masters degree holder earns= (108000-45,000)

a masters degree holder earns=$63000

the average= (54000+63000)/2

the average= (117000)/2

the average=$58500

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2 years ago

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Answer:

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2 years ago

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Step-by-step explanation:

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3 years ago

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Find the unit rate for 18 oz box

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3 years ago

Find the dimensions of a rectangle (in m) with area 1,000 m2 whose perimeter is as small as possible. (Enter the dimensions as a

Amanda [17]

The perimeter of the rectangle is the sum of its dimensions

The dimensions that minimize the perimeter are $\mathbf{10\sqrt{10 },10\sqrt{10 }}$

The area is given as:

$\mathbf{A = 1000}$

Let the dimension be x and y.

So, we have:

$\mathbf{A = xy = 1000}$

Make x the subject

$\mathbf{x = \frac{1000}{y}}$

The perimeter is calculated as:

$\mathbf{P = 2(x + y)}$

Substitute $\mathbf{x = \frac{1000}{y}}$

$\mathbf{P = 2(\frac{1000}{y} + y)}$

Expand

$\mathbf{P = \frac{2000}{y} + 2y}$

Differentiate

$\mathbf{P' = -\frac{2000}{y^2} + 2}$

Set to 0

$\mathbf{ -\frac{2000}{y^2} + 2 = 0}$

Rewrite as:

$\mathbf{ -\frac{2000}{y^2} = -2}$

Divide both sides by -1

$\mathbf{\frac{2000}{y^2} = 2}$

Multiply y^2

$\mathbf{2000 = 2y^2}$

Divide by 2

$\mathbf{1000 = y^2}$

Take square roots of both sides

$\mathbf{y = \sqrt{1000 }}$

$\mathbf{y = 10\sqrt{10 }}$

Substitute $\mathbf{y = \sqrt{1000 }}$ in $\mathbf{x = \frac{1000}{y}}$

$\mathbf{x = \frac{1000}{\sqrt{1000}}}$

$\mathbf{x = \sqrt{1000}}$

$\mathbf{x = 10\sqrt{10 }}$

Hence, the dimensions that minimize the perimeter are $\mathbf{10\sqrt{10 },10\sqrt{10 }}$