Solve by the linear combination method (with or without multiplication). 2x+3y=11 - 4x+2y=2

Well, the first one is pretty simple, you want to be able to eliminate one of the variables. In this case, the y's will cancel each other out.

x + y = 5

x - y = 7

Add the two equations straight down.

---x + x = 2x

---y - y = 0y * The y's canceled each other out, which is what you want!*

---5 + 7 = 12

2x + 0y = 12

2x = 12

Divide both sides by 2

x = 6

Now you know that x = 6. In order to find y, let x = 6 for either of your original equations. I would recommend checking both equations, to make sure you get the same y value.

x + y = 5

(6) + y = 5

6 + y = 5

Subtract 6 from both sides

y = - 1

x - y = 7

(6) - y = 7

6 - y = 7

Subtract 6 from both sides

-y = 1

y cannot be negative. Divide both sides by - 1 to make y positive.

y = - 1

You get the same value for y in both equations when you let x = 6. * You want this!*

Your answer:

x = 6

y = - 1

(6,-1)