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multiply the first equation by 3 , then add them together...
The basic rules are, you can multiply an equation by a constant value rearrange equations and add equations together...
@DanJS what do you mean multiply them?
If you multiply an entire equation by a constant number, the equation is unchanged... \[3*[4x-y=-11]\]
So when you do that then add the two together, a variable goes to zero and drops out
The result after multiplying the first by 3 is there, and now add the two together... 12x - 3y = -33 2x + 3y = 5 ------------------
14x = -29
you want to find a number you can multiply each equation by, so that when added together, you have a variable drop out. In this case -3y + 3y = 0y
@DanJS so I would have to do this to each one ?
Here i will do each basic step for this example.....
4x - 1y = -11 2x + 3y = 5 If added together, you just will get 6x + 2y = -6
you see that so far?
yes I see @DanJS
ok, so think of some number you can multiply one of the equations by , so that when added will result in zero for one variable...
if you multiply the first by 3, you will have a -3y in the first and a +3y in the second
you see what i mean ?
3*[4x - y = -11] 1*[2x + 3y = 5] ------------------- that is the same as the original, you can multiply both sides of the equation by a number
@DanJS yes I see! so it would leave me with Answer B correct??
no, lets continue....
If you carry out what is above.. you get 12x - 3y = -11 2x + 3y = 5 ---------------- That was the point, now when added the y term goes to zero
sorry 12x - 3y = -33 2x + 3y = 5 ------------------
now add them together, both sides of the equals
right !, remember those two basic rules... and the goal of getting a variable to go to zero like the Y did here
Multiplying an equation by a constant number, and Adding two equations together... that is it
@DanJS this really helped, thank you for explaining this to me!
I could type all the dumb script rules in, but those are the ideas
One step further.....
Say you have one that has terms on the Y like this ... 3y = 10 ... 2y = 41
How to get those to add and cancel out... multiply the first by +2 Multiply the second by -3
6y -6y ----- 0y
just take care of the X and right side of the = when you multiply through and add too
That is it... good luck
@DanJS wow you make this very easy, definitely writing these in my notes! thank you so much!
welcome, practice.. hehe