To find the solution to the system of equations \( y = 52x - 4 \) and \( y = -12x + 5 \), you need to determine where the two lines intersect. The intersection point represents the solution to the system.
You can set the equations equal to each other to find the x-coordinate of the intersection:
\[ 52x - 4 = -12x + 5 \]
Now, combine like terms:
\[ 52x + 12x = 5 + 4 \]
\[ 64x = 9 \]
Now, solve for \( x \):
\[ x = \frac{9}{64} \]
Next, substitute \( x \) back into either equation to find the corresponding \( y \)-coordinate. Let's use the first equation:
\[ y = 52\left(\frac{9}{64}\right) - 4 \]
Calculating this:
\[ y = \frac{468}{64} - 4 = \frac{468}{64} - \frac{256}{64} = \frac{212}{64} = \frac{53}{16} \]
So, the solution to the system of equations is:
\[ \left( \frac{9}{64}, \frac{53}{16} \right) \]
Thus, the response is:
\[ \left( \frac{9}{64}, \frac{53}{16} \right) \]