values (x,y) for a system of quadratic equations

[Guest]

consider the system of quadratic equations

y = 3x^2 - 5x
y = 2x^2 - x - c

a) For what values of c will the system have more than one real solution (x,y)?
B) For what values of c will the system have no real solutions (x,y)?

Please address the x and y values for each part. Thanks!

[Guest]

A) c<4
B) c>4

[Guest]

Since this is your problem is there some reason you did not show any attempt of your own to do this? It would help to at least know where you had difficulty.

It should be obvious that one way to determine whether or not a problem has a unique answer, no answer, or more than one answer is to try to solve it!

If [tex]y= 3x^2- 5x[/tex] and [tex]y= 2x^2- x- c[/tex] then [tex]3x^2- 5x= 2x^2- x- c[/tex].

Subtract [tex]2x^2[/tex] from each side and add [tex]x+ c[/tex] to both sides:
[tex]x^2- 4x+ c= 0[/tex].

That's a quadratic equation so may have no solution, one solution, or two solutions.
Solve it using the quadratic formula:
[tex]x= \frac{4\pm\sqrt{16- 4c}}{2}= \frac{4\pm\sqrt{4(4- c)}}{2}=
\frac{4\pm 2\sqrt{4- c}}{2}= 2\pm\sqrt{4- c}[/tex].

Now, when does this have no (real number) solution, one solution, or more than one solution?