Tom determines the system of equations below has two solutions, one of which is located at the vertex of the parabola. equation 1: (x – 3)2 = y – 4 equation 2: y = -x + b in order for this solution to be reasonable, which qualifications must be met? b must equal 7 and a second solution to the system must be located at the point (2, 5). b must equal 1 and a second solution to the system must be located at the point (4, 5). b must equal 7 and a second solution to the system must be located at the point (1, 8). b must equal 1 and a second solution to the system must be located at the point (3, 4).

Step-by-step explanation:

The given functions are

First, we need to express the quadratic function in the form

Through, we can deduct the vertex, which is at . So, in this case

This means, if the system has one solution located at the vertex of the parabola, then the line must pass through such point as the image attached shows.

In addition, if , then the equation of the line would be

Which is the exact equation to have two solutions in this no linear system. As you can observe in the image, this line intercept the parabola at two points, at (2,5) and at vertex (3,4)

Therefore, the right answer is the first choice.

2/3

step-by-step explanation:

the slope of a line is equal to the rise/run. in this case the line rises 2 units for every +3 units it moves