Solve the system of equations. show your work. y = x^2 - 3x + 4 and x + y = 4

This is a parabola intercepted by a straight line. It will have 0, 1 or 2 solutions.

If you convert the straight line to y = 4-x, and fill it in to the first one, you get:

4-x = x^2-3x+4
x^2 - 2x = 0
x(x-2) = 0
x = 0 or x=2

Great! We didn't even need the quadratic formula.

Fill in these x values in either formula (or both to double check!) to find that (0,4) and (2,2) are the solutions. Put differently:

x=0, y=4 and x=2, y=2 are the solutions.

7.07 (3 significant figures)

Step-by-step explanation:

the distance between the two points on the x axis is 5 and the distance between the two point son the y axis is 5. thus by using pythagerous theorem you are able to get the hypotenuse which is the distance between the two points which in this case is 7.07 when rounded to 3 significant figures. not sure if im correct but i hope it helps