What is the solution set for the following system of equations?

(-2, -5) and (1,4)

Step-by-step explanation:

The simpler equation is the second:  it gives y as the linear function 3x + 1.  Substitute this 3x + 1 for y in the first equation, obtaining

3x + 1 = x^2 + 4x - 1.  

Move all terms from the left to the right:  x^2 + 4x - 1 - 3x - 1, or:

x^2 + x - 2 = 0, which is in the form of a quadratic equation.  

Factoring this equation, we get:

x^2 + x - 2 = 0.  This factors as follows:  (x+2)(x-1) = 0, so x = -2 and x = 1.

Now subst. 1 for x in y = 3x + 1:  y = 3(1) + 1, or y = 4.  Thus, (1,4) is one point of intersection of the two graphs.  Next, find y for x = -2:  y = 3(-2) + 1, or -5.

Thus, the 2 points of intersections of the graphs are (-2,-5) and (1,4).

no

step-by-step explanation: