Intersections and systems

The solution of a system of equations is the point where their graphs cross.

Example: the two lines $3x + 2y = 12$ and $x - y = -1$. Click where they cross, and Desmos shows $(2, 3)$, so $x = 2$ and $y = 3$.

• You don't need to rearrange into $y = \ldots$ form. Desmos graphs equations in any form.
• No intersection (parallel lines) means no solution. The same line twice means infinitely many solutions.
• For a line and a parabola, count the crossing points to answer "how many solutions?" questions.

On the test: if the question asks for $x + y$ or $2x - y$, find the intersection first, then compute. There is no need to solve it symbolically.