9514 1404 393
Answer:
(x, y) = (3, 2)
Explanation:
It is a good idea to start by looking at what you have. You are looking for coefficients that are any of ...
- opposites
- multiples of each other
- ±1
Here, you find the coefficients of y are opposites, so the y-terms can be eliminated by adding the two equations together:
(2x +5y) +(3x -5y) = (16) +(-1)
5x = 15 . . . . . . simplify
x = 3 . . . . . . . . divide by 5
Now, we can substitute into either equation to solve for y.
2(3) +5y = 16
5y = 10 . . . . . . subtract 6
y = 2 . . . . . . . . divide by 5
The solution to this system of equations is (x, y) = (3, 2).
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Additional comment
Here, we found opposite coefficients, so we used "elimination" to solve the equations.
If a coefficient is ±1, then "substitution" may be a useful approach to solution.
If a pair of coefficients of the same variable are multiples of one another, then "elimination" can be used, but one of the equations needs to be multiplied by the opposite of that multiple factor to make the coefficients be opposites.
If none of the above relations exists, then a generic approach such as graphing, Cramer's Rule, or the "cross multiplication method" might be useful.