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Solve using substitution. x + 2y = 7 2x − y = –16Asked by ..
Solve using substitution.
x+2y=7
2x-y=-16
x+2y=7
2x-y=-16
Answers
Answered by
GPT-4o mini
To solve the system of equations using substitution, we start with the two given equations:
1. \( x + 2y = 7 \) (Equation 1)
2. \( 2x - y = -16 \) (Equation 2)
First, solve Equation 1 for \( x \):
\[
x = 7 - 2y
\]
Now that we have \( x \) in terms of \( y \), we can substitute this expression for \( x \) into Equation 2:
\[
2(7 - 2y) - y = -16
\]
Now distribute the \( 2 \):
\[
14 - 4y - y = -16
\]
Combine like terms:
\[
14 - 5y = -16
\]
Next, isolate \( y \) by subtracting 14 from both sides:
\[
-5y = -16 - 14
\]
\[
-5y = -30
\]
Now, divide both sides by -5:
\[
y = \frac{-30}{-5} = 6
\]
Now that we have the value of \( y \), we can substitute it back into the expression we found for \( x \):
\[
x = 7 - 2(6)
\]
\[
x = 7 - 12
\]
\[
x = -5
\]
Thus, the solution to the system of equations is
\[
x = -5, \quad y = 6
\]
So the final answer is:
\[
\boxed{(-5, 6)}
\]
1. \( x + 2y = 7 \) (Equation 1)
2. \( 2x - y = -16 \) (Equation 2)
First, solve Equation 1 for \( x \):
\[
x = 7 - 2y
\]
Now that we have \( x \) in terms of \( y \), we can substitute this expression for \( x \) into Equation 2:
\[
2(7 - 2y) - y = -16
\]
Now distribute the \( 2 \):
\[
14 - 4y - y = -16
\]
Combine like terms:
\[
14 - 5y = -16
\]
Next, isolate \( y \) by subtracting 14 from both sides:
\[
-5y = -16 - 14
\]
\[
-5y = -30
\]
Now, divide both sides by -5:
\[
y = \frac{-30}{-5} = 6
\]
Now that we have the value of \( y \), we can substitute it back into the expression we found for \( x \):
\[
x = 7 - 2(6)
\]
\[
x = 7 - 12
\]
\[
x = -5
\]
Thus, the solution to the system of equations is
\[
x = -5, \quad y = 6
\]
So the final answer is:
\[
\boxed{(-5, 6)}
\]
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