Question

The triangle on the left has a perimeter of 14. The triangle on the right has a perimeter of 21. What are x and y?

Answer 1

2y+x=14 and 10/4y+3x=21 correct?
Systems equation then.

10/4y+3x=21 simplifies to 10y+12x=84. A little big, but stick with it and it looks nice and pretty in the end.

The other equation needs to be arranged so that the variable with 1 as a coefficient (just to make it easier) is all by itself on one side of the equation. So, by subtracting 2y from both sides, we get x=-2y+14. Now it starts to get a little messier, but I promise it gets easier after this.

Now that you know x, you can plug it into your other equation, so instead of 10y+12x=84 you get 10y+12(-2y+14)=84. Now you can multiply out the 12 and simplify, leaving you with 10y-24y+168=84, which simplifies to -14y=-84 and ultimately x=6

Now that we know x, we can go all the way back to our first equation and plug it in. So, (6)+2y=14 simplifies to 2y=8 and then y=4.

In a coordinate pair, your answer would be (6,4) (All of my teachers expected this notation).

Hope this helps, it's a little long but it's not hard. :)

Answer 2

Thank you so much! :)

Answer 3

Yep, glad it helped!