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3 years ago

Solve the simultaneous equations 2x+y=5 5x+3y=12

Mathematics

1 answer:

Bezzdna [24]3 years ago

5 0

Answer:

x=3 and y= -1

Step-by-step explanation:

Step 1: Solve2x+y=5 for y:

2x+y=5

2x+y+−2x=5+−2x(Add -2x to both sides)

y=−2x+5

Step 2: Substitute−2x+5foryin5x+3y=12:

5x+3y=12

5x+3(−2x+5)=12

−x+15=12(Simplify both sides of the equation)

−x+15+−15=12+−15(Add -15 to both sides)

(Divide both sides by -1)

x=3

Step 3: Substitute3forxiny=−2x+5:

y=−2x+5

y=(−2)(3)+5

y=−1(Simplify both sides of the equation)

Answer:

x=3 and y=−1

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Answer:

19.0% (1dp)

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2 years ago

The top and bottom margins of a poster are 6 cm and the side margins are each 8 cm. If the area of printed material on the poste

Degger [83]

Answer:

The total height and width of the poster is approximately 28.93 and 38.57.

Step-by-step explanation:

Consider the provided information.

Let us consider the width and length of the printed part of the poster is x and y respectively.

For better understanding refer the figure 1:

The area of the printed part is 382 cm²

Area = xy = 382

y = 382/x

Now the total height of the poster is y + 6 + 6 = y + 12

Total width of the poster is x + 8 + 8 = x + 16

Thus the total area of the poster is:

A = (x + 16)(y + 12)

Now substitute the value of y in above equation.

$A = (x+16)(\frac{382}{x}+12)$

$A = 382+12x+\frac{6112}{x}+192$

$A = 12x+\frac{6112}{x}+574$

Now differentiate the above equation with respect to x.

$A' = 12-\frac{6112}{x^2}$

Now, substitute A'= 0 and solve for x.

$0 = 12-\frac{6112}{x^2}$

$12=\frac{6112}{x^2}$

$x^2=\frac{6112}{12}$

$x=22.57$ Ignore the negative value of x as width can't be a negative number.

Now find A''

$A'' = \frac{2(6112)}{x^3}$

Here A" is positive for x>0 and x = 22.57 is minimum.

Use the value of x to find all the respective dimensions of the poster.

Substitute the value of x in y = 382/x

y = 382/22.57 = 16.93

The total height of the poster is y + 6 + 6 = y + 12 = 16.93 + 12 = 28.93

Total width of the poster is x + 8 + 8 = x + 16 = 22.57 + 16 = 38.57

Hence, the total height and width of the poster is approximately 28.93 and 38.57.

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3 years ago

Read 2 more answers

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3 years ago

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Step-by-step explanation:

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