Asked by bloozoo
Solve the system of equations.
x−3y=18
7x−5y=46
(1 point)
Responses
(−3, −5)
left parenthesis negative 3 comma negative 5 right parenthesis
(105, 5)
left parenthesis 105 comma 5 right parenthesis
(33, 5)
left parenthesis 33 comma 5 right parenthesis
(3, −5)
x−3y=18
7x−5y=46
(1 point)
Responses
(−3, −5)
left parenthesis negative 3 comma negative 5 right parenthesis
(105, 5)
left parenthesis 105 comma 5 right parenthesis
(33, 5)
left parenthesis 33 comma 5 right parenthesis
(3, −5)
Answers
Answered by
GPT-4o mini
To solve the system of equations given by:
1. \( x - 3y = 18 \) (Equation 1)
2. \( 7x - 5y = 46 \) (Equation 2)
We will use the substitution method. First, we will solve Equation 1 for \( x \):
\[ x = 3y + 18 \]
Now we can substitute this expression for \( x \) into Equation 2:
\[ 7(3y + 18) - 5y = 46 \]
Distributing the 7:
\[ 21y + 126 - 5y = 46 \]
Combine like terms:
\[ 16y + 126 = 46 \]
Now, isolate \( y \):
\[ 16y = 46 - 126 \]
\[ 16y = -80 \]
\[ y = -5 \]
Now that we have \( y \), we can substitute it back into the expression we found for \( x \):
\[ x = 3(-5) + 18 \]
\[ x = -15 + 18 \]
\[ x = 3 \]
So the solution to the system of equations is \( (3, -5) \).
The correct response is:
**(3, −5)**
1. \( x - 3y = 18 \) (Equation 1)
2. \( 7x - 5y = 46 \) (Equation 2)
We will use the substitution method. First, we will solve Equation 1 for \( x \):
\[ x = 3y + 18 \]
Now we can substitute this expression for \( x \) into Equation 2:
\[ 7(3y + 18) - 5y = 46 \]
Distributing the 7:
\[ 21y + 126 - 5y = 46 \]
Combine like terms:
\[ 16y + 126 = 46 \]
Now, isolate \( y \):
\[ 16y = 46 - 126 \]
\[ 16y = -80 \]
\[ y = -5 \]
Now that we have \( y \), we can substitute it back into the expression we found for \( x \):
\[ x = 3(-5) + 18 \]
\[ x = -15 + 18 \]
\[ x = 3 \]
So the solution to the system of equations is \( (3, -5) \).
The correct response is:
**(3, −5)**
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