how to solve a system by addition?

Question

how would you solve by addition?
2x+3y=1
5x+3y=16

Answer 1

You add the two equations together, just like adding anything else--line up the x's adn y's and numbers vertically. Eliminate one of the variables (x or y) by finding a common coefficient (in your case, y already has a common coefficient (3). Mulitply one equation by -1 (changing all the pos/neg signs). Add your equations, thus eliminating one variable (y in your case), then solve the remainder for x. Once you have x, you can then solve for y.

Answer 2

Multiply everything in the top equation by -1. You have:
-2x - 3y = -1
5x + 3y = 16

Add the like terms in the two equations together. You get:
3x = 15 (because the y's cancel).

Solve for "x":
x = 5
Plug 5 in for x into either of the original equations to find y.
2(5) + 3y = 1
10 + 3y = 1
3y = -9
y = -3

So your answer is (5,-3)

Answer 3

Step 1: Subtract the second equation from the first equation:
5x+3y=16
- 2x+3y=1
-----------------------------
3x + 0y = 15
x = 5

Step 2: Use the value of X to find Y.
2(5) + 3y = 1
3y = -9
y = -3