To find a solution to the system of equations \( y = 23x - 5 \) and \( y = 73x - 1 \), we can set the two equations equal to each other:
\[ 23x - 5 = 73x - 1 \]
Now, let's solve for \( x \).
First, we can rearrange the equation to isolate \( x \):
\[ -5 + 1 = 73x - 23x \] \[ -4 = 50x \]
Now, divide by 50:
\[ x = -\frac{4}{50} = -\frac{2}{25} \]
Next, we can substitute \( x = -\frac{2}{25} \) back into one of the original equations to find \( y \). We'll use the first equation:
\[ y = 23\left(-\frac{2}{25}\right) - 5 \] \[ y = -\frac{46}{25} - 5 \] \[ y = -\frac{46}{25} - \frac{125}{25} \] \[ y = -\frac{171}{25} \]
So, the solution to the system of equations is:
\[ \left(-\frac{2}{25}, -\frac{171}{25}\right) \]
If you have specific points you want to verify as solutions, please provide those points, and I can check if they solve the system.
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