Help with points of intersection

[Bruh]

Is some able to show me how to find the points of intersection of the line y+6x=11 and the parabola y=x^2-8x+12

 

[Steven G]

In the first equation you listed replace y with x^2-8x+12. Please do that and post your work showing as far as you got with that.

 

[Deleted member 4993]

Is some able to show me how to find the points of intersection of the line y+6x=11 and the parabola y=x^2-8x+12

You have parabola (y = x^2 - 8x +12) and a straight line (y = -6x + 11). I'll show you how to do the general problem.

parabola \(\displaystyle \ \to \ \) y = A*x^2 + B*x + C

straight line \(\displaystyle \ \to \ \) y = D*x + E

Where A, B, C, D & F are constants.

Let the point of intersection be (x₁,y₁). Then:

y₁ = A*(x₁)^2 + B*x₁ + C .......................................from the parabola and

y₁ = D*x₁ + E .......................................from the straight-line

equating the y₁ above, we get:

A*(x₁)^2 + B*x₁ + C = D*x₁ + E

A * (x₁)^2 + [B - D] *x₁ + [C - E] = 0

You can solve for x₁ from the quadratic equation above. Continue......

If you are still stuck, come back and tell us exactly where you are getting lost.