Solve this linear system using the elimination method.

3x – y = 3

x + y = 17

Good heavens, the y's are already lined up and signed up for us to eliminate them.

(3x + x) + (-y + y) = (3 + 17)

4x = 20

x = 5

Plug x = 5 into the second original equation and solve for y.

5 + y = 17

y = 12

The solution seems to be (5, 12). Let's make a quick check for body doubles, evil clones, or demonic possession.

3x – y = 3

3(5) – 12 = 3?

Yes, it checks out.

Solve this linear system using the elimination method.

2x + 3y = 4

3x – 2y = 6

Multiply the first equation by 2 and the second equation by 3, and then add them together to clear the equations of y.

4x + 6y = 8

9x – 6y = 18

Addition time:

(4x + 9x) + (6y – 6y) = (18 + 8)

13x = 26

x = 2

Plug x = 2 into one of the original equations and solve for the missing y.

2x + 3y = 4

2(2) + 3y = 4

4 + 3y = 4

3y = 0

y = 0

The solution is (2, 0). But now we gotta check it. Use 3x – 2y = 6.

Does 3(2) – 2(0) = 6 – 0 = 6?

Just maybe. Okay, it does. There's no fooling you.

Solve the system of linear equations using the elimination method.

Hey, who came in here and jumbled up our equations?

That's better. Now, would we rather try to multiply and eliminate some simple whole numbers, like with x, or tango with a snarl full of fractions with y? We'll stick with x, thank ya much. Multiply the first equation by -3:

And add the two equations together:

How about that: everything cancels out.

0 = 0

We have a true statement without any variables. So, we have an infinite number of solutions to our system of equations. These equations represent the same line.

Solve the system of linear equations using the elimination method.

9x = y – 4

Start off by lining the equations up in the same form.

y = 9x + 4

Uh oh, our spidey sense is tingling. Two equations with the same slope but different y-intercepts? Sounds like a case of parallel lines to us. Let's multiply the second equation through by -1 to check.

-y = -9x – 4

Now add both equations:

-y = -9x – 4

Yep, these are parallel lines, so there are no solutions to the system.