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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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