Verify that the dominant term in the operation count (number of multiplications or number of additions) for solving a lower tria
ngular system of order n by forward substitution is n^2 /2.
1 answer:
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Answer:
(x, y) = (4, 1)
Step-by-step explanation:
The coefficients of x are the same, so we can cancel the x-terms by subtracting one equation from the other. We want to do this so the resulting y-coefficient will be positive. That means we want to subtract the second equation from the first:
(-2x +y) -(-2x -4y) = (-7) -(-12)
5y = 5 . . . . . . . . simplify
y = 1 . . . . . . . . divide by 5
-2x +1 = -7 . . . . . substitute for y in the first equation
-2x = -8 . . . . . subtract 1
x = 4 . . . . . . divide by -2
The solution is (x, y) = (4, 1).
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A graphing calculator easily verifies the solution.
