Question

The system of equations y=52x−4 and y=−12x+5 is shown on the graph below. According to the graph, the solution to the system of equations is (Response area, Response area).Skip to navigation

Answer 1

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:

\[
\left( \frac{9}{64}, \frac{53}{16} \right)
\]