SOLUTION: -4c minus 2d equals -2 (first equation)
2c minus 2d equals -14 (second equation)
how do i solve this? the section is calle elimination using adding and subtracting
Question 257696: -4c minus 2d equals -2 (first equation)
2c minus 2d equals -14 (second equation)
how do i solve this? the section is calle elimination using adding and subtracting Found 2 solutions by richwmiller, jsmallt9:Answer by richwmiller(17219) (Show Source):
The key to the elimination method is to find or create opposites for one of the variables. As your systems stands, -4c and 2c are not opposites of each other. Neither are -2d and -2d. It is nice when your system starts off with opposotes for one of the variables lined up. But when this does not happen we need to find a way to create opposites. This involves multiplying one or both equations by numbers that you choose so that opposites are lined up.
Probably the simplest way to get opposites is to multiply either equation by -1. This will turn the -2d into +2d which is the opposite of the -2d that remains in the other equation. It doesn't matter which equation we multiply by -1 in this system. I will multiply the first equation (because it will not only get opposites but it will eliminate 3 minus signs). After multiplying the first equation by -1 are system is:
Now that we have opposites (2d and -2d) lined up, we can add the two equations together. When we do so, the opposites will cancel each other out. After adding the two left sides and the two right sides together we get the following equation:
By getting the opposites lined up and adding the equations, we end up with an equation that has only one variable in it. (This is the "elimination" of the elimination method.) This one variable equation is easy to solve:
It is easy to feel that we are finished. But this is a system of two variable equations. The solution will be an ordered pair with a number for c and a number for d. We still need to find d. We can use our value for c and one of the original equations to find d. It doesn't matter which equation we use. I'll use the first:
Substituting our value for c into this equation we get:
which simplifies to:
Subtracting 8 from each side we get:
Dividing both sides by -2 we get:
Our solution, found with the elimination method, is (-2, 5)
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