Let's analyze the given system of linear equations:
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The first equation is: \[ y = 7x + 8 \]
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The second equation simplifies as follows: \[ -7 + y = -8 \] Adding 7 to both sides: \[ y = -1 \]
Now we have the system:
- \( y = 7x + 8 \)
- \( y = -1 \)
To find the intersection of these two equations, we can set them equal to each other: \[ 7x + 8 = -1 \]
Solving for \( x \): \[ 7x = -1 - 8 \] \[ 7x = -9 \] \[ x = -\frac{9}{7} \]
Now substituting \( x = -\frac{9}{7} \) back into either equation to find \( y \): Using \( y = -1 \): \[ y = -1 \]
Thus, we have a single solution: \[ \left(-\frac{9}{7}, -1\right) \]
This means that the system of linear equations has exactly one solution.
Thus, the answer is 1.