Please help me solve this...Thanks in advance

Question

Solve the system of equations: y = -x^3 + (3/4)x^2 + (3/2)x + (1/2) y = -x^2 + x + (1/2)

Answer 1

We can equate the two functions of x, because they are both equal to y:

-x^3+(3/4)x^2+(3/2)x+1/2=-x^2+x+1/2;

x(-x^2+(7/4)x+1/2)=0;

4x(-4x^2+7x+2)=0; 4x(4x^2-7x-2)=0=4x(4x+1)(x-2), x=0, 2 or -1/4.

For each value of x we have the following values for y:

1/2, -3/2, 3/16