Answer:
x = 19/4, y = 1/2
Explanation:
To solve using the elimination method, first set the two equations out like this:
2x + y = 10
2x - y = 9
Now subtract the bottom equation from the first one, going through each term separately.
2x - (2x) + y - (-y) = 10 - (9)
∴ 2y = 1
y = 1/2
As you can see, this method works well when either the x value or y value in both equations are the same, as this leads to one of them cancelling out (the x in this case) leaving only the y. Now we simply substitute this y value back into one of the original two equations to find x. Hence:
2x + y = 10
2x + 1/2 = 10
2x = 19/2
x = 19/4
Hope that helps!