Linear-Quadratic Lock

Solve Simultaneous Equations Step-by-Step

Small Integers Large Integers Decimals

Step 1: Equate

Since both equal $y$, set them equal to each other:

Step 2: Rearrange to Zero

Move everything to one side to form $Ax^2 + Bx + C = 0$.

$x^2 +$ $x +$ $= 0$

Step 3: Find x values

Solve the quadratic for $x$ (Factorise or Formula).

$x_1 =$

$x_2 =$

Step 4: Find Coordinates

Which equation is easier to substitute into?

Mastering simultaneous equations bridges algebra and geometry.

Main System

"At the intersection points, the y-value from the line is the same as the y-value from the curve. That's why we can write Line = Curve!"