Given the system of equations:
x + y = 2
3x - 4y = 27
Let's eliminate x in the system and find the result when the two equations are added.
To eliminate the x variable, let's multiply each equation by the value that makes the coefficients of x opposite.
Let's multiply equation 1 by -3:
(-3x) + (-3y) = -3(2)
3x - 4y = 27
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-3x - 3y = -6
3x - 4y = 27
Add both equations:
-3x - 3y = -6
+ 3x - 4y = 27
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- 7y = 21
Therefore, after eliminating the x variable, the result is:
-7