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SashulF [63]
3 years ago
13

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

Mathematics
2 answers:
ollegr [7]3 years ago
8 0

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

<u>the answer Part 1) is the option A </u>

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

The system has no solution

therefore

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

There is no x value as there is no solution to the system.

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

6x-6=6

6x=12

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

we know that

x+y=1,120

x=1,120-y -------> equation A

3x-2y=1,300 ------> equation B

substitute equation A in equation B

3[1,120-y]-2y=1,300

3,360-5y=1,300

5y=3,360-1,300

5y=2,060

y=412

therefore

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

y=412

nekit [7.7K]3 years ago
5 0
1) <span>D. There is no x value as there is no solution to the system 

2) </span><span>D. There is no x value as there is no solution to the system. 

3) </span><span>D. 2
</span>

4x + 2y = 6 ; x – y = 3

x = 3 + y

4(3+y) + 2y = 6

12 + 4y + 2y = 6

6y = 6 – 12

6y = -6

y = -1

x = 3 + (-1)

x = 2

4) D. 412

x = one-step equation

y = two-step equation

x + y = 1120

3x – 2y = 1300

X = 1120 – y

3(1120 – y) – 2y = 1300

3360 – 3y -2y = 1300

-5y = 1300 – 3360

-5y = -2060

Y = 412  two-step equation

X = 1120 – 412

X = 708  one-step equation.



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Answer:

Since Darcie wants to crochet a minimum of 3 blankets and she crochets at a rate of 1/5 blanket per day, we can determine how many days she will need to crochet a minimum of 3 blankets following the next steps:

- Finding the number of days needed to crochet one (1) blanket:

\begin{gathered}1=\frac{1}{5}Crochet(Day)\\Crochet(Day)=5*1=5\end{gathered}

1=

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Crochet(Day)=5∗1=5

So, she can crochet 1 blanket every 5 days.

- Finding the number of days needed to crochet three (3) blankets:

If she needs 5 days to crochet 1 blanket, to crochet 3 blankets she will need 15 days because:

\begin{gathered}DaysNeeded=\frac{NumberOfBlankets}{Rate}\\\\DaysNeeded=\frac{3}{\frac{1}{5}}=3*5=15\end{gathered}

DaysNeeded=

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- Writing the inequality

If she has 60 days to crochet a minimum of 3 blankets but she can complete it in 15 days, she can skip crocheting 45 days because:

AvailableDays=60-RequiredDaysAvailableDays=60−RequiredDays

AvailableDays=60-15=45DaysAvailableDays=60−15=45Days

So, the inequality will be:

s\leq 45s≤45

The inequality means that she can skip crocheting a maximum of 45 days since she needs 15 days to crochet a minimum of 3 blankets.

Have a nice day!

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3 years ago
Find n(A) for the following set. <br> A={a,b,c,...,z}
MariettaO [177]

n(A) = 26

Solution:

Let us first define the cardinal number of the set.

Cardinal number of the set:

The number of distinct elements in a finite set is called its cardinal number. It is denoted as n(A).

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We know that, there are 26 elements in the alphabet "a to z".

Number of elements in the set A = 26

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soldi70 [24.7K]

Hello!

Distributive property: a(b+c)=ab+ac

a=-7, b=y, c=2

-7y-(-7)*2

Minus and plus sign.

-7y+7*2

Then multiply by the numbers.

7*2=14

\boxed{=-7y+14}

Hope this helps!

Thanks!

Have a great day!

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3 years ago
(2.0 x 10-3) (3.5 x 10)<br> What is the value of the expression?
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Answer:

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Step-by-step explanation:

SOLUTION STEPS

(2.0×10−3)(3.5×10)

Multiply 2 and 10 to get 20.

(20−3)×3.5×10

Subtract 3 from 20 to get 17.

17×3.5×10

Multiply 17 and 3.5 to get 59.5.

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Multiply 59.5 and 10 to get 595.

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Answer:

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