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SashulF [63]
2 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]2 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]2 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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emmasim [6.3K]
<h2>Hello!</h2>

The answer is:

They spent $176 together.

<h2>Why?</h2>

We are given an expression which represents the money spent for each girl, it's a function of time and it will show how much they can spend in terms of hours.

Assuming that you have committed a mistake writing the equation, otherwise, the given options would not fit, the expression is:

p(t)=5x^{4}-3x^{3}+2x^{2}+24

Now, from the statement we know that the function represents how much money each girl spent, so, if we need to calculate how much money they will spend together, we need to multiply the expression by 2, so we have:

p(t)=2(5x^{4}-3x^{3}+2x^{2}+24)

Then, calculating the spent money for 2 hours, we need to substitute the variable "x" with 2.

Calculating we have:

p(2)=2(5*(2)^{4}-3*(2)^{3}+2*(2)^{2}+24)=2(5*16-3*8+2*4+24)

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Hence, we have that they spent $176 together.

Have a nice day!

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