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:

$$(\frac{9}{64},\frac{53}{16})$$

Thus, the response is:

$$(\frac{9}{64},\frac{53}{16})$$