To solve the system of equations by substitution, we need to organize the given steps in a logical sequence. Let's analyze the steps provided and arrange them accordingly:
-
Write one equation in terms of x or y:
Start with the equation \( x - 2y = 11 \) and solve for x:
\( x = 2y + 11 \)
This corresponds to:
\( x - 2y = 11 \rightarrow x = 2y + 11 \) -
Substitute that expression into the other equation:
Now substitute \( x = 2y + 11 \) into the first equation \( 7x - 2y = -13 \):
So you can express it as:
\( 7(2y + 11) - 2y = -13 \)
This corresponds to:
\( -7(2y + 11) - 2y = -13 \) (but the signs seem to be mixed with the original equation here). -
Simplify the substituted equation:
Simplify:
\( 14y + 77 - 2y = -13 \) (Note: The step provided with negative signs appears to be incorrect, so this is the correct change in signs). This leads to:
\( 12y + 77 = -13 \) -
Combine like terms:
Move the constant to the other side:
\( 12y = -13 - 77 \)
This results in:
\( 12y = -90 \) -
Solve for y:
Dividing both sides by 12 gives:
\( y = -4 \) -
Substitute back to find x:
Now substitute \( y = -4 \) back into the equation \( x = 2y + 11 \):
\( x = 2(-4) + 11 \)
Which results in:
\( x = -8 + 11 \)
\( x = 3 \) -
Write the solution as an ordered pair:
Thus, the solution to the system of equations is:
\( (3, -4) \)
Putting these steps in order, we get:
- \( x - 2y = 11 \rightarrow x = 2y + 11 \)
- Substitute: \( 7(2y + 11) - 2y = -13 \)
- Simplify: \( 14y + 77 - 2y = -13 \)
- Combine: \( 12y = -90 \)
- Solve for y: \( y = -4 \)
- Substitute back: \( x = 2(-4) + 11 \)
- Final solution: \( (3, -4) \)
Note: Some of the indicated steps in your list contained errors with sign and simplification; I've corrected them for a coherent solution process.
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