 When we solve by elimination, what we want to do is pick one variable to eliminate. We can either eliminate the x's or eliminate the y's, and we can multiply an entire equation by a number that we get, both the positive and the negative coefficients in front of either the x's or the y's. So you can eliminate whatever you want. Looking at this equation, or these two equations up here, I'm going to go ahead and pick to eliminate the y's. The only reason why I'm saying that is because I'm noticing that I have a positive 3y and a negative 4y. So I have my positives and negatives set. We certainly could eliminate for the x's. We actually might be dealing with smaller numbers, but it's all going to give us the same answer in the end. So I'm going to eliminate the y's, and I want to think what number, I'm looking at the 3 and the negative 4. What number do they both go into, multiples of 3? I want to get those up to 12, a positive 12y and a negative 12y. So I'm going to multiply our first equation by a positive 4. I need to make sure I remember to multiply everything, both sides of the equal sign, by that 4. So when we rewrite it, we have 8x plus 12y equals 48. Then the bottom equation, the blue one, I need to get this negative 4y up to a negative 12. So I'm just going to multiply it by 3, distribute the 3 to everything. So 3 times 3x is 9x, 3 times a negative 4y is a negative 12y. That's what I wanted to get, and then 3 times 1 is 3. What we're going to do now is we're going to add these two equations together. 8x plus 9x is 17x. The 12y plus the negative 12y, that actually equals 0, so it cancels away, and that's what we were looking for. And so this equals 48 plus 3 is 51. So now I have a much simpler equation to solve for x. I'm going to go ahead and divide both sides by the 17, and x equals 3. So we have one of our variables. To get the other one, all that we have to do is go back to one of our equations. It doesn't matter which one and substitute in a 3 for the x. I'll go ahead and pick just this first one. I don't know why I could use any of them. So I have a 2 times, now that I know what x is, I can go ahead and plug in a 3. 2 times 3 plus 3y equals 12. So we have a 6 plus 3y equals 12. Subtract 6 from both sides, 3y equals 12 minus 6 is 6. Divide both sides by 3, so y is equal to a 2. So the solution for this system, we always want to write our answer as a point. The x value is a 3, and the y value is a 2. So these two lines cross at the point 3, 2. We could check our answer by plugging 3, 2 into both the blue and the red equations to make sure that we get a true statement. But there is your elimination example.