Question

I am giving 10 points to whoever completes these answers correctly

1.y = –3x + 6
y = 9
What is the solution to the system of equations?

A.(–21, 9)
B.(9, –21)
C.(–1, 9)
D.(9, –1)


2.What is the solution to the system of equations?
y=2/3x+3
x=-2

A.(-2 - 15/2)
B.(-2,5/3)
C.(-2,11/6)
D.(-2,13/3)

3.What is the solution to the system of equations?
y=1/3x-10
2x+y=4

A.(–8, 6)
B.(–6, 16)
C.(6, –8)
D.(16, –6)

4.Ernesto tried to determine the solution for the system of equations using substitution. His work is shown below.

x – y = 7

3x – 2y = 8

Step 1: x = y + 7
Step 2: 3(y + 7) – 2y = 8
Step 3: 3y + 7 – 2y = 8
Step 4: y + 7 = 8
Step 5: y = 1

In which step did Ernesto make the first error?

A.Step 1
B.Step 2
C.Step 3
D.Step 4

Answer 1

1-c (-1,9)

2-b(-2,5/3)

3-c(6,-8)

4-c step 3

Answer 2

Part 1) we have

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

`y=9` ------> equation B

Equate equation A and equation B

`9=-3x+6`

Solve for x

`3x=6-9`

`x=-3/3=-1`

the solution is the point
`(-1,9)`

therefore

the answer part 1) is the option C

`(-1,9)`

Part 2) we have

`y=(2)/(3)x+3` ------> equation A

`x=-2` ------> equation B

Substitute equation B in equation A

`y=(2)/(3)*(-2)+3`

`y=-(4)/(3)+3`

`y=(5)/(3)`

the solution is the point
`(-2,(5)/(3))`

therefore

the answer Part 2) is the option B

`(-2,(5)/(3))`

Part 3) we have

`y=(1)/(3)x-10` ------> equation A

`2x+y=4` ------> equation B

Substitute equation A in equation B

`2x+(1)/(3)x-10=4`

`(7)/(3)x=14`

`x=14*3/7=6`

Find the value of y

`y=(1)/(3)x-10`

`y=(1)/(3)*6-10=-8`

the solution is the point
`(6,-8)`

therefore

the answer Part 3) is the option C

`(6,-8)`

Part 4) we have

`x-y=7` ------> equation A

`3x-2y=8` ------> equation B

Step 1

Isolate the variable x in the equation A

`x=y+7` -------> new equation A

Step 2

Substitute the new equation A in the equation B

`3[y+7]-2y=8`

Step 3

Solve for y

`3y+21-2y=8` ------> In this step Ernesto make the first error

Step 4

Combine like terms in the left side

`y+21=8`

Step 5

Subtract
`21` both sides

`y+21-21=8-21`

`y=-13`

therefore

the answer Part 4) is the option C

Step 3