how to solve X*2+2x-3=kx*3-6x*2=bx-6 find k and b

Question

i havent a clue how to do this

Answer 1

Combining the 1st and 3rd equations:

x^2+2x-3-bx+6=0; x^2+(2-b)x+3=0; x=(b-2+sqrt(b^2-4b+4-12))/2=(b-2+sqrt(b^2-4b-8))/2. If b=-2, x=(-4+2)/2=-1 or -3.

Combining 1st and 2nd equations:

kx^3-6x^2-x^2-2x+3=0; kx^3-7x^2-2x+3=0;

Put x=-1, b=-2 in kx^3-6x^2-bx+6=0 and -k-6-2+6=0, so k=-2.

Put x=-3, b=-2 and -27k-54-6+6=0 and -27k-54=0, so k=-2.

These results are consistent for b and k, despite different values for x. All equations have been used so b=k=-2.