What is the best approximate solution for the system of linear equations: y = 15x + 1 and y = 1?

To find the best approximate solution of the system of linear equations given by:

We can start by substituting the expression for y from Equation 2 into Equation 1.

Since Equation 2 states that y = 1, we can substitute this value into Equation 1:

1 = 15x + 1

Next, we simplify this equation to find the value of x:

1 - 1 = 15x

0 = 15x

From this result, we see that:

x = 0

Now that we have the value of x, we can substitute it back into either original equation to find y. Using Equation 2, we have:

y = 1

Thus, we find the solution:

(x, y) = (0, 1)

In conclusion, the best approximate solution for the given system of linear equations is:

(x, y) = (0, 1)

This means that at the point (0, 1), both equations intersect, therefore it satisfies both conditions of the system.