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2 years ago

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Kerry invited 23 friends to his pool party. They played a game where everyone had to separate into groups. Each group had the sa

me number of children. The game could not be played with all 24 children in one group, and each group had to have more than 2 children.
Which of the following are ways that they could divide into groups? Select all that apply.

A.
They can form 4 groups of 6.

B.
They can form 12 groups of 2.

C.
They can form 8 groups of 3.

D.
They can form 4 groups of 9.

E.
They can form 2 groups of 12.

1 answer:

Alex17521 [72]2 years ago

6 0

Answer:

A, C, and E are the answers

Step-by-step explanation:

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1. What is the value of the y variable in the solution to the following system of equations?

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Part 1)

we have

$3x-6y=3$ ------> equation A

$7x-5y=-11$ ------> equation B

Multiply by $-7$ the equation A

$-7(3x-6y)=-7*3$

$-21x+42y=-21$ ------> equation C

Multiply by $3$ the equation B

$3*(7x-5y)=-11*3$

$21x-15y=-33$ -------> equation D

Adds equation C and equation D

$-21x+42y=-21 \\21x-15y=-33\\---------- \\ 42y-15y=-21-33\\27y=-54 \\ y=-2$

therefore

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$y=-2$

Part 2)

we have

$3x+y=6$

$y=-3x+6$ ------> equation A

$6x+2y=8$

Simplify Divide by $2$ both sides

$3x+y=4$

$y=-3x+4$ ------> equation B

the lines A and B are parallel lines, because the slope m is equal

so

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therefore

<u>the answer Part 2) is the option D</u>

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Part 3)

we have

$4x+2y=6$ ------> equation A

$x-y=3$

$y=x-3$ ------> equation B

substitute equation B in equation A

$4x+2[x-3]=6$

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$x=2$

therefore

<u>the answer part 3) is the option D</u>

$x=2$

Part 4)

Let

x---------> The number of one-step equations

y---------> The number of two-step equations

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therefore

<u>the answer part 4) is the option D</u>

$y=412$

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