Well, it says method of your choice, which means substitution or elimination (addition). Now, a lot of the time the first thing you check for is if the x's or the y's look like multiples of each other. For example, if I invent two equations like:
3x -9y = 18
5x + 27y = 24
Now, it may not always be obvious, but what I notice is that 9 times 3 is 27. And since we have a -9y and a positive 27y, I can multiply thetop equation by 3 to give me
9x - 27y = 54
5x + 27y = 24
Now I can add the two equations and eliminate y. So if you can see that a variable might be eliminated easily, you probably want to choose elimination method. Now on to what we actually have:
4x - 3y = 6
-12x + 9y = -24
So again, the first thing Im checking for is if either the x's or the y's are multiples of one another. If you notice, we have a +4 and a -12. Well, 4 times 3 = 12, so that's pretty easy to see. And you can maybe see this with the y's, too. We have a -3y and a +9y. Well, 9 is 3 times 3, so the y's can match up easily as well. So it looks like elimination is a good strategy.
Now just to clarify, when we do the elimination method, we are multiplying one or both of the equations (all of the numbers in each equation) by some number in order to get x's and y's in both equations to be the same number, but of opposite signs. After you accomplish this, you then add both equations together. X's get added to X's, y's to y's, numbers to numbers. So the goal is to get a
3x
-3x or
9y
-9y
something as to where if we were to add the two, they would become 0. So now like I mentioned, it does look liek x's can be matched up pretty easily. So I currently have:
4x and
-12x
If I multiply 4x by 3, I will have 12x and -12x. Because of this, I'm going to multiply that whole top equation by 3. Doing this I get:
12x - 9y =18
-12x + 9y = -24
Now I add the two equations. So I have -12x + 12x = 0. -9y + 9y = 0. 18 + -24 = -6 to get a final result of
0 +0 = -6.....
Clearly there is no possible way this can happen. Whenever you get two things on opposite sides of the equal sign that are never equal, there are no solutions. Kinda make sense?