How do you solve 2x – y = 4, 3x + y = 1 by graphing?

$\left(1 , - 2\right)$

Explanation:

A line represents a series of solutions for a given equation. Where you have 2 equations, you have 2 lines. Where those lines intersect is the point that serves as a solution for both equations.

The first graph looks like:

graph{2x-4 [-10, 10, -5, 5]}

and the second like this:

graph{-3x+1 [-10, 10, -5, 5]}

If we compare the two graphs, we'll see that the point $\left(1 , - 2\right)$ is common to both lines, so that is the solution.

In real life, using graph paper, you can graph both functions on one sheet of paper and see the intersection without having to compare back and forth.