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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

Respuesta :

1-c (-1,9)

2-b(-2,5/3)

3-c(6,-8)

4-c step 3

calculista

Part 1) we have

[tex]y=-3x+6[/tex] ------> equation A

[tex]y=9[/tex] ------> equation B

Equate equation A and equation B

[tex]9=-3x+6[/tex]  

Solve for x

[tex]3x=6-9[/tex]  

[tex]x=-3/3=-1[/tex]  

the solution is the point [tex](-1,9)[/tex]

therefore

the answer part 1) is the option C

[tex](-1,9)[/tex]

Part 2) we have

[tex]y=\frac{2}{3}x+3[/tex] ------> equation A

[tex]x=-2[/tex] ------> equation B

Substitute equation B in equation A

[tex]y=\frac{2}{3}*(-2)+3[/tex]

[tex]y=-\frac{4}{3}+3[/tex]

[tex]y=\frac{5}{3}[/tex]

the solution is the point [tex](-2,\frac{5}{3})[/tex]

therefore

the answer Part 2) is the option B

[tex](-2,\frac{5}{3})[/tex]

Part 3) we have

[tex]y=\frac{1}{3}x-10[/tex] ------> equation A

[tex]2x+y=4[/tex] ------> equation B

Substitute equation A in equation B

[tex]2x+\frac{1}{3}x-10=4[/tex]  

[tex]\frac{7}{3}x=14[/tex]  

[tex]x=14*3/7=6[/tex]  

Find the value of y

[tex]y=\frac{1}{3}x-10[/tex]

[tex]y=\frac{1}{3}*6-10=-8[/tex]

the solution is the point [tex](6,-8)[/tex]

therefore

the answer Part 3) is the option C

[tex](6,-8)[/tex]

Part 4) we have

[tex]x-y=7[/tex] ------> equation A

[tex]3x-2y=8[/tex] ------> equation B

Step 1

Isolate the variable x in the equation A

[tex]x=y+7[/tex] -------> new equation A

Step 2

Substitute the new equation A in the equation B

[tex]3[y+7]-2y=8[/tex]

Step 3

Solve for y

[tex]3y+21-2y=8[/tex] ------> In this step Ernesto make the first error

Step 4

Combine like terms in the left side

 [tex]y+21=8[/tex]

Step 5

Subtract [tex]21[/tex] both sides

 [tex]y+21-21=8-21[/tex]

 [tex]y=-13[/tex]

therefore

the answer Part 4) is the option C

Step 3