Using Desmos calculator to find solutions to system of equations

Desmos is a free graphing calculator you can use on the SAT.
You type each equation on a numbered row in the left panel, and Desmos instantly draws it on the grid to the right.
To solve a system, enter both equations and look at where their graphs meet — that intersection is the solution.
Click the point and Desmos labels its coordinates.

The picture tells you how many solutions there are.
If the graphs cross once, there is one solution; if they are parallel and never meet, there is no solution; if the two equations draw the exact same line, there are infinitely many.

Desmos only understands the letters $x$ and $y$.
So if a problem uses other letters, rename them before typing — for a system in $m$ and $n$, replace $m$ with $x$ and $n$ with $y$.
Then read the intersection's coordinates back as the values of $m$ and $n$.

You can also use Desmos to check a point.
Type the point in as $(2, 1)$ along with the equations, and see which graph passes right through it.
This is handy when a question asks which line or curve a given point lies on.

Desmos shades inequalities too, which is perfect for systems of inequalities.
Type each inequality and Desmos shades the region where it is true; the darker region where the shadings overlap is the solution.
You can then read off which quadrant that overlap falls in.

It is just as useful when one equation is a curve.
For a line and a parabola, enter both and the crossing points are the solutions.
If the line only touches the parabola at one point, that single point is the solution — often the vertex.

You graph $y = 3x + 4$ and $y = 4x + 4$ in Desmos. How many solutions does the system have?
The two lines have different slopes, so they cross at exactly one point.
So the system has one solution, at the crossing point $(0, 4)$.

Two equations are graphed in Desmos and turn out to be parallel, never touching. How many solutions does the system have?
Parallel lines never intersect, and the solution is the intersection.
So the system has no solution.

A system uses the letters $m$ and $n$, but Desmos only accepts $x$ and $y$. How do you graph it?
Replace $m$ with $x$ and $n$ with $y$, then type the two equations and find where they cross.
Read the intersection's coordinates back as the values of $m$ and $n$.