Solve this system of equations by graphing.

y = 3x – 3

-4x + 2y = -6

Let's start off by graphing our lines. One is in slope-intercept form, with m = 3 and b = -3, and the other is in standard form with intercepts of (1.5, 0) and (0, -3).

Jackpot. We have a clear intersection at the y-intercept, (0, -3). We already know they're both on the line, so we're done. If only we could catch breaks like that more often.

Solve this system of equations by graphing.

y = 3x

y = 2x + 1

Both of these lines are in slope-intercept form already. The first has a y-intercept of (0, 0), with a rise of 3 and run of 1. The second passes through (0, 1), rising and running by 2 / 1.

The cafes are busy this time of day, so that must be why they meet at (1, 3) instead. We check our answer by plugging the point back into the equations.

3 = 3(1)

3 = 2(1) + 1

We are golden.

Solve this system of equations by graphing.

The slope for both of these lines is , but they have different y-intercepts. That sounds like an open-and-shut case of parallel lines to us, but let's check the graph.

The lines are parallel. They don't intersect. There is no solution.

Solve this system of equations by graphing.

y = -1

y = 2x + 1

Didn't we just graph y = 2x + 1 like two problems ago? Guess it's back for round 2.

As for the first equation, y = -1 will equal -1 for every value of y, regardless of what x equals. That makes it a horizontal line.

They're meeting up at (-1, -1). That makes sense, because y = -1 refuses to go anywhere that doesn't have a -1 for y. That's a nasty case of agoraphobia. Let's check the other equation, though.

-1 = 2(-1) + 1

Don't panic, y = -1. Everything is okay.