SOLUTION: how many solutions does {y=4x+1, y=x^2+4} have? 0,1,2,or 3

 

It's a line and a parabola, There could 0, 1, or 2 solutions.
3 is not possible

Let's graph the two equations:



Looks like there are two solutions.

We'll do it algebraically and see:



Since both are solved for y, we can
set their right sides equal



Get 0 on the left



Switch sides:



Factor:



Use zero-factor principle:

; 
  ; 

Now we get the corresponding y coordinates
by substituting each in 

Substituting x=3






So one solution is (x,y) = (3,13)

Substituting x=1






So the other solution is (x,y) = (1,5)

It looks right from the graph:



Edwin