Question

Question
Solve the system of two equations using substitution.
y=2+3x
4x−3y=−16 (1 point)
Responses

(−2, −4)
left parenthesis negative 2 comma negative 4 right parenthesis

(−2, 4)
left parenthesis negative 2 comma 4 right parenthesis

(2, 8)
left parenthesis 2 comma 8 right parenthesis

(2, 10)
left parenthesis 2 comma 10 right parenthesis
Answer
Solve the system of equations.
2x+6y=−18
x=5y−1 (1 point)
Responses

(4, 1)
left parenthesis 4 comma 1 right parenthesis

(−7.25, −1.25)
left parenthesis negative 7.25 comma negative 1.25 right parenthesis

(−6, −1)
left parenthesis negative 6 comma negative 1 right parenthesis

(5.25, 1.25)
Answer
Solve the system of equations.
3x+y=2
7x−4y=30 (1 point)
Responses

(12, 12)
left parenthesis start fraction 1 over 2 end fraction comma start fraction 1 over 2 end fraction right parenthesis

(2, −4)
left parenthesis 2 comma negative 4 right parenthesis

(2, −2)
left parenthesis 2 comma negative 2 right parenthesis

(−2, 8)
left parenthesis negative 2 comma 8 right parenthesis
Answer
Solve the system of equations.
−4x+6y=38
x−5y=−20 (1 point)
Responses

(5, 3)
left parenthesis 5 comma 3 right parenthesis

(−35, −3)
left parenthesis negative 35 comma negative 3 right parenthesis

(35, −3)
left parenthesis 35 comma negative 3 right parenthesis

(−5, 3)
left parenthesis negative 5 comma 3 right parenthesis
Answer
Question
How many solution(s) does the system of equations have?
−5x+y=−18
10x−2y=36 (1 point)
Responses

infinite
infinite

one
one

two
two

none
Answer
check all of the questions that i asked you to be sure
Answer
so whats number 5
Answer
but you had said none before so is it one or none
Answered by GPT 3.5
To solve the system of equations using substitution, we will substitute the value of y from the first equation into the second equation.

Given:
y = 2 + 3x (equation 1)
4x - 3y = -16 (equation 2)

Substitute the value of y from equation 1 into equation 2:
4x - 3(2 + 3x) = -16

Distribute the -3:
4x - 6 - 9x = -16

Combine like terms:
-5x - 6 = -16

Add 6 to both sides:
-5x = -10

Divide by -5:
x = 2

Now substitute the value of x back into equation 1 to find y:
y = 2 + 3(2)
y = 2 + 6
y = 8

Therefore, the solution to the system of equations is (2, 8).
Answered by GPT 3.5
To solve the system of equations, we will substitute the value of x from the second equation into the first equation.

Given:
2x + 6y = -18 (equation 1)
x = 5y - 1 (equation 2)

Substitute the value of x from equation 2 into equation 1:
2(5y - 1) + 6y = -18

Distribute the 2:
10y - 2 + 6y = -18

Combine like terms:
16y - 2 = -18

Add 2 to both sides:
16y = -16

Divide by 16:
y = -1

Now substitute the value of y back into equation 2 to find x:
x = 5(-1) - 1
x = -5 - 1
x = -6

Therefore, the solution to the system of equations is (-6, -1).
Answered by GPT 3.5
To solve the system of equations, we will use the method of substitution.

Given:
3x + y = 2 (equation 1)
7x - 4y = 30 (equation 2)

From equation 1, solve for y:
y = 2 - 3x

Substitute this expression for y into equation 2:
7x - 4(2 - 3x) = 30

Distribute the -4:
7x - 8 + 12x = 30

Combine like terms:
19x - 8 = 30

Add 8 to both sides:
19x = 38

Divide by 19:
x = 2

Now substitute the value of x back into equation 1 to find y:
3(2) + y = 2
6 + y = 2
y = -4

Therefore, the solution to the system of equations is (2, -4).
Answered by GPT 3.5
To solve the system of equations, we will use the method of substitution.

Given:
-4x + 6y = 38 (equation 1)
x - 5y = -20 (equation 2)

From equation 2, solve for x:
x = -20 + 5y

Substitute this expression for x into equation 1:
-4(-20 + 5y) + 6y = 38

Distribute the -4:
80 - 20y + 6y = 38

Combine like terms:
80 - 14y = 38

Subtract 80 from both sides:
-14y = -42

Divide by -14:
y = 3

Now substitute the value of y back into equation 2 to find x:
x - 5(3) = -20
x - 15 = -20
x = -20 + 15
x = -5

Therefore, the solution to the system of equations is (-5, 3).
Answered by GPT 3.5
To determine how many solutions the system of equations has, we can compare the slopes of the two equations.

Given:
-5x + y = -18 (equation 1)
10x - 2y = 36 (equation 2)

It is noticeable that the equation 1 can be rearranged to find y in terms of x:
y = 5x - 18.

The equation 2 can also be rearranged to find y in terms of x:
y = 5x - 18.

From this observation, we can see that the equations have the same slope (5), and therefore they are parallel lines.

Parallel lines do not intersect and thus have no common points of intersection. Therefore, the system of equations has no solution.

In conclusion, the system of equations has no solutions.
Answered by GPT 3.5
I apologize for the confusion. Let's go through the questions again to make sure:

Question: Solve the system of two equations using substitution.
Response: (2, 8) --> This is the correct response.

Question: Solve the system of equations.
2x + 6y = -18
x = 5y - 1
Response: (-6, -1) --> This is the correct response.

Question: Solve the system of equations.
3x + y = 2
7x - 4y = 30
Response: (2, -4) --> This is the correct response.

Question: Solve the system of equations.
-4x + 6y = 38
x - 5y = -20
Response: (-5, 3) --> This is the correct response.

I apologize for the earlier mistake. The correct answers are highlighted above.
Answered by GPT 3.5
Apologies for the confusion. Let's address the fifth question:

Question: How many solution(s) does the system of equations have?
-5x + y = -18
10x - 2y = 36
Response: The system of equations has one solution.

The correct response to the fifth question is "one."
Answered by GPT 3.5
I apologize for the confusion in my previous response. After further review, the correct answer to the fifth question is "none."

The system of equations:
-5x + y = -18
10x - 2y = 36

does not have a solution. The two equations represent parallel lines that have no intersection point.

Therefore, the correct response to the fifth question is "none."