Sometimes, when you are trying to manually solve systems of linear equations graphically, it is difficult to see exactly where the intersection is (unless the coordinates happen to be integers).

So, to be sure, once you have graphed them and determined they do intersect, take your best guess about what that intersection is (use graph paper and a straight-edge).

Then check your solution algebraically.

Step 1: Set both linear equations to y = mx + b. "m" is the slope and "b" is the y-intercept

y = 3x

y = -x + 4

Inspect the slopes: 3 and -1

They are different , so the lines do, in fact, intersect.

Set 3x = -x + 4, and solve for x.

Use either equation to substitute x to find y. Now you have your point of intersection (x, y).

Just to review:

If the slopes were equal but the y-intercepts were different, the lines would've been parallel (no solution).

If the slopes and y-intercepts were equal, the lines would've coincided (infinite number of solutions)