Asked by bloozoo
Solve the system of equations.
8x−4y=−28
2x−6y=8
(1 point)
Responses
(−5,−3)
left parenthesis negative 5 comma negative 3 right parenthesis
(−2, 3)
left parenthesis negative 2 comma 3 right parenthesis
(−4,−1)
left parenthesis negative 4 comma negative 1 right parenthesis
(7, 1)
8x−4y=−28
2x−6y=8
(1 point)
Responses
(−5,−3)
left parenthesis negative 5 comma negative 3 right parenthesis
(−2, 3)
left parenthesis negative 2 comma 3 right parenthesis
(−4,−1)
left parenthesis negative 4 comma negative 1 right parenthesis
(7, 1)
Answers
Answered by
GPT-4o mini
To solve the system of equations:
1. \( 8x - 4y = -28 \)
2. \( 2x - 6y = 8 \)
we can use either the substitution method or the elimination method. Here, I'll use the elimination method.
First, we can simplify the first equation:
\[
8x - 4y = -28 \implies 2x - y = -7 \quad \text{(dividing the entire equation by 4)}
\]
Now our system of equations looks like this:
1. \( 2x - y = -7 \)
2. \( 2x - 6y = 8 \)
Next, we'll express \( y \) in terms of \( x \) from the first equation:
\[
y = 2x + 7
\]
Now we will substitute \( y \) in the second equation:
\[
2x - 6(2x + 7) = 8
\]
Expanding this gives:
\[
2x - 12x - 42 = 8
\]
Combining like terms results in:
\[
-10x - 42 = 8
\]
Next, we will isolate \( x \):
\[
-10x = 8 + 42 \implies -10x = 50 \implies x = -5
\]
Now that we have \( x \), we can find \( y \) by substituting \( x = -5 \) back into \( y = 2x + 7 \):
\[
y = 2(-5) + 7 = -10 + 7 = -3
\]
Therefore, the solution to the system of equations is:
\[
(x, y) = (-5, -3)
\]
So the correct response is:
\[
\text{(−5,−3)}
\]
1. \( 8x - 4y = -28 \)
2. \( 2x - 6y = 8 \)
we can use either the substitution method or the elimination method. Here, I'll use the elimination method.
First, we can simplify the first equation:
\[
8x - 4y = -28 \implies 2x - y = -7 \quad \text{(dividing the entire equation by 4)}
\]
Now our system of equations looks like this:
1. \( 2x - y = -7 \)
2. \( 2x - 6y = 8 \)
Next, we'll express \( y \) in terms of \( x \) from the first equation:
\[
y = 2x + 7
\]
Now we will substitute \( y \) in the second equation:
\[
2x - 6(2x + 7) = 8
\]
Expanding this gives:
\[
2x - 12x - 42 = 8
\]
Combining like terms results in:
\[
-10x - 42 = 8
\]
Next, we will isolate \( x \):
\[
-10x = 8 + 42 \implies -10x = 50 \implies x = -5
\]
Now that we have \( x \), we can find \( y \) by substituting \( x = -5 \) back into \( y = 2x + 7 \):
\[
y = 2(-5) + 7 = -10 + 7 = -3
\]
Therefore, the solution to the system of equations is:
\[
(x, y) = (-5, -3)
\]
So the correct response is:
\[
\text{(−5,−3)}
\]
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