The idea behind elimination is to add or subtract the equations, or multiples of the equations from each other to get rid of one of the variables. When adding or subtracting equations,you add the left sides and the right sides together, and the new expression will still be equal. So here, we want to set up the equations so that we either have the same number of y's or the same number of x's in the two equations. In our first equation we have 2x, so we can multiply both sides of the second equation by 2 to also have 2x there. I.E 2(x+2y) = 2 (-5), so 2x +4y = -10. Now we have 2x in each equation, and we subtract them. This gives (2x-3y) - (2x + 4y) = (-25 - (-10)), so -7y = -15, and y = 15/7. We can then plug this into either original equation to get x = -65/7.
May 11th, 2015
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