## Sophia.13 Group Title Part 1 (3 points) : When solving systems of equations, how do you determine what method to use? Part 2 (10 points) : Choose 1 system of equations from the choices below. Then, solve the system and post your solution, showing your steps so that other students can see which method you chose. –y + 3x = 6 y = –6x + 12 6x – 4y = 54 –9x + 2y = –69 2y = x + 1 –2x – y = 7 one year ago one year ago

1. srossd

For part 1, it's basically whatever looks like it will be easiest. If you have a -5x in one equation and a 5x in the other, it's probably easiest to add them together. If you can easily solve for x or y, then substitution is probably easiest. But it doesn't matter if you don't make the best choice here, because each method will give you the correct answer.

2. srossd

For part 2, I'll work through the first one, and then you can try one of the others to make sure you understand. Here, we have that case I mentioned - a y in one of them, and a -y in the other. So I'll add them together, and get \[3x=-6x+18\] \[9x=18\] So x=2. Plug that back in to either equation, and you'll see that y=0.

3. Sophia.13

So for part two, if i chose elimination what would i have to do?

4. srossd

This is embarrassing, but I don't know the names of all these methods, I just do em. What's elimination exactly?

5. srossd

If I remember correctly, it's just adding equations together like I did.

6. Sophia.13

yes

7. Sophia.13

2y = x + 1 –2x – y = 7 For this equation^

8. abb0t

matrices

9. srossd

You could use matrices, but that's overcomplicating things here.

10. srossd

When you don't have a nice matchup like 2x and -2x, you'll have to multiply one of them by something first. So for this example, multiply the top (or the bottom, but I'm choosing the top arbitrarily) by 2 and then add: 4y = 2x+2 -2x-y=7 4y+7=2-y 5y=-5 y=-1 Then plug that back in, and you'll get x=-3.