What is the solution to the system of equations y = 3x + 8 and y = 5x + 2?

To find the solution to the system of equations y = 3x + 8 and y = 5x + 2, we need to determine the values of x and y that simultaneously satisfy both equations. This can be done using the substitution method or the elimination method. Here, we will use the substitution method.

First, we can set the two equations equal to each other since they both equal y:

3x + 8 = 5x + 2

Now, we will solve for x. Start by isolating x on one side:

3x + 8 - 2 = 5x

6 = 5x - 3x

6 = 2x

x = 3

Now that we have the value for x, we can substitute it back into either of the original equations to find the corresponding value for y. We’ll use the first equation:

y = 3(3) + 8

y = 9 + 8

y = 17

Thus, the solution to the system of equations is (x, y) = (3, 17).

In summary, the intersection point of the two lines represented by the equations is at the coordinates (3, 17).