Question 252265
Since x+1 = y AND y=x^2-4x+7, x+1 = x^2-4x+7

This equation can be rewritten as 0 = x^2-5x+6.

This equation can be factored into linear expressions so x^2-5x+6=(x-3)*(x-2)=0

So x=3 and x = 2.

Next each of values for x can be substituted in either equation to determine the values of y.

Using the equation y = x +1.

When x = 2, y = 2+1 = 3

When x = 3, y = 3+1 = 4.

So, there are two solutions to the system of equations.

You may want to graph both equation to "see" the points of intersection of the two graphs.