Asked by Lee Hooni 🖤
Solve the system of equations.
−4x+6y=38
x−5y=−20 (1 point)
Responses
(35, −3)
left parenthesis 35 comma negative 3 right parenthesis
(−5, 3)
left parenthesis negative 5 comma 3 right parenthesis
(5, 3)
left parenthesis 5 comma 3 right parenthesis
(−35, −3)
−4x+6y=38
x−5y=−20 (1 point)
Responses
(35, −3)
left parenthesis 35 comma negative 3 right parenthesis
(−5, 3)
left parenthesis negative 5 comma 3 right parenthesis
(5, 3)
left parenthesis 5 comma 3 right parenthesis
(−35, −3)
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve the system of equations
\[
-4x + 6y = 38 \quad (1)
\]
\[
x - 5y = -20 \quad (2)
\]
we can use substitution or elimination. Here, we will use substitution.
From equation (2), we can express \( x \) in terms of \( y \):
\[
x = 5y - 20
\]
Now, we substitute this expression for \( x \) into equation (1):
\[
-4(5y - 20) + 6y = 38
\]
Distributing \(-4\):
\[
-20y + 80 + 6y = 38
\]
Combine like terms:
\[
-20y + 6y + 80 = 38
\]
\[
-14y + 80 = 38
\]
Now isolate \( y \):
\[
-14y = 38 - 80
\]
\[
-14y = -42
\]
Dividing both sides by \(-14\):
\[
y = 3
\]
Now substitute \( y \) back into the expression we found for \( x \):
\[
x = 5(3) - 20
\]
\[
x = 15 - 20
\]
\[
x = -5
\]
Thus, the solution to the system is:
\[
(x, y) = (-5, 3)
\]
The correct response is:
\[
\boxed{(-5, 3)}
\]
\[
-4x + 6y = 38 \quad (1)
\]
\[
x - 5y = -20 \quad (2)
\]
we can use substitution or elimination. Here, we will use substitution.
From equation (2), we can express \( x \) in terms of \( y \):
\[
x = 5y - 20
\]
Now, we substitute this expression for \( x \) into equation (1):
\[
-4(5y - 20) + 6y = 38
\]
Distributing \(-4\):
\[
-20y + 80 + 6y = 38
\]
Combine like terms:
\[
-20y + 6y + 80 = 38
\]
\[
-14y + 80 = 38
\]
Now isolate \( y \):
\[
-14y = 38 - 80
\]
\[
-14y = -42
\]
Dividing both sides by \(-14\):
\[
y = 3
\]
Now substitute \( y \) back into the expression we found for \( x \):
\[
x = 5(3) - 20
\]
\[
x = 15 - 20
\]
\[
x = -5
\]
Thus, the solution to the system is:
\[
(x, y) = (-5, 3)
\]
The correct response is:
\[
\boxed{(-5, 3)}
\]
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.