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Inga [223]
3 years ago
7

1/2x+1/4y=6. 1/5x+1/3y=1

Mathematics
2 answers:
Savatey [412]3 years ago
8 0
<u>1st Step:</u>

\frac { 1 }{ 2 } x+\frac { 1 }{ 4 } y=6\\ \\ 4\left( \frac { 1 }{ 2 } x+\frac { 1 }{ 4 } y \right) =6\cdot 4\\ \\ 2x+y=24\\ \\ y=24-2x

<u>2nd Step:</u>

\frac { 1 }{ 5 } x+\frac { 1 }{ 3 } y=1\\ \\ 15\left( \frac { 1 }{ 5 } x+\frac { 1 }{ 3 } y \right) =1\cdot 15

\\ \\ 3x+5y=15\\ \\ 5y=15-3x\\ \\ 5y=3\left( 5-x \right) \\ \\ y=\frac { 3\left( 5-x \right)  }{ 5 }

<u>3rd Step:</u>

\frac { 3\left( 5-x \right)  }{ 5 } =24-2x

\\ \\ 5\cdot \frac { 3\left( 5-x \right)  }{ 5 } =5\left( 24-2x \right) \\ \\ 3\left( 5-x \right) =120-10x

\\ \\ 15-3x=120-10x\\ \\ -3x+10x=120-15\\ \\ 7x=105\\ \\ x=\frac { 105 }{ 7 }

\\ \\ \therefore \quad x=15

<u>4th Step (When x=15):</u>

y=24-2\left( 15 \right) \\ \\ y=24-30\\ \\ \therefore \quad y=-6
Ierofanga [76]3 years ago
3 0
\frac{1}{2}x+\frac{1}{4}y=6 \ \ \ |\times 2 \\&#10;\frac{1}{5}x+\frac{1}{3}y=1 \ \ \ |\times (-5) \\ \\&#10;x+\frac{1}{2}y=12 \\&#10;\underline{-x-\frac{5}{3}y=-5} \\&#10;\frac{1}{2}y-\frac{5}{3}y=12-5 \\&#10;\frac{3}{6}y-\frac{10}{6}y=7 \\&#10;-\frac{7}{6}y=7 \\&#10;y=7 \times (-\frac{6}{7}) \\&#10;y=-6 \\ \\&#10;x+\frac{1}{2}y=12 \\&#10;x+\frac{1}{2} \times (-6)=12 \\&#10;x-3=12 \\&#10;x=12+3 \\&#10;x=15 \\ \\&#10;\boxed{(x,y)=(15,-6)}
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Sedbober [7]

Answer:

The correct answer is Adam rowed faster in the men's 500-meter kayak race.

Step-by-step explanation:

To find the speed he rowed in both races, you need to divide the distance of the race by the time it took him to finish. In the first race, he rowed 500 meters and did it in a time of 1 minute 37.9 seconds, so the speed in that race would be \frac{500}{97.9} or approximately 5.10725 meters per second. In the second race, Adam rowed a distance of 1000 meters and did it in a time of 3 minutes 28.2 seconds, which means his speed in that race would be \frac{1000}{208.2} or approximately 4.80307 meters per second. Since his speed in the first race was faster than his speed in the second race, Adam rowed faster in the first race would be the correct answer.

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Answer:

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Step-by-step explanation:

-2x(3 - 5x)

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The senior classes at High School A and High School B planned separate trips to Lake Compounce. The senior class at High School
storchak [24]

Answer:

Number of students in vans =15 and bus =46

Step-by-step explanation:

use variables for the vans and buses

let x= vans and y=buses

Now solve the 2 equations simultaneously

<em><u>remember</u></em><em><u> </u></em><em><u>to</u></em><em><u> </u></em><em><u>number</u></em><em><u> </u></em><em><u>your</u></em><em><u> </u></em><em><u>equations</u></em>

6x+7y=412..........1

6x+9y=504.........2

make x the subject of one equation

and label it equation 3

6x=412—7y

x =  \frac{206}{3}  -  \frac{7y}{6} .............3

subs 3 into 2

6( \frac{206}{3}  -  \frac{7y}{6} ) + 9y = 504

412 - 7y + 9y = 504

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subs 4 into 1

6x + 7(46) = 412

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6x = 412 - 322

6x = 90

x = 15

Therefore there are 15 students in each van and 46 students in each bus.

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Step-by-step explanation:

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