Graph both sides and intersect

Turn any equation or system into two graphs and let Desmos find where they meet.

When to use it

Solving a system of equations
Solving an equation that's hard to do by hand, like $\sqrt{x + 7} = x - 5$ or $500(1.04)^x = 800$
Word problems that ask when two quantities are equal

1Type the left side on one line and the right side on the next. You can skip $y =$ : Desmos graphs $x^2 - 3$ the same as $y = x^2 - 3$ .
2Click either graph. Desmos marks every intersection with a gray point.
3Click a gray point to see its coordinates. The x-coordinate is the solution.

Example · loaded in the calculator

Solve $x^2 - 3 = 2x$ .

The graphs cross at $(-1, -2)$ and $(3, 6)$ , so $x = -1$ or $x = 3$ .

The calculator is already set up with this example. Click the graphs and edit the expressions to explore.

Watch out

If you don't see an intersection, zoom out. Exponential and word-problem graphs often meet far from the origin.

Check your understanding

To solve $\sqrt{x + 4} = x - 2$ in Desmos, what should you graph?

Try it: edit the example

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How to do it

1Type the left side on one line and the right side on the next. You can skip

y =

: Desmos graphs

x^2 - 3

the same as

y = x^2 - 3

2Click either graph. Desmos marks every intersection with a gray point.

3Click a gray point to see its coordinates. The x-coordinate is the solution.