9514 1404 393
Answer:
B. The substitution method is the best choice because one of the variables in one equation has a coefficient of 1
Explanation:
We find the easiest choice to be using a graphing calculator (see attached). It shows the solution to be (x, y) = (94, 234).
__
The only coefficient with a magnitude of 1 is the coefficient of y in the second equation. That coefficient is -1, not 1. The only coefficients related by an integer are the coefficients of y: the coefficient of y in the first equation is a multiple of that in the second equation.
Strictly speaking, none of the answer choices matches the reasoning.
__
We could use substitution, because the coefficient of y in the second equation is -1.
y = 2x+46
5x -2(2x +46) = 2
x = 2+92 = 94
y = 2(94) +46 = 234
The solution by substitution is (x, y) = (94, 234).
__
We could use elimination, because the coefficient of y in the first equation is a multiple of the coefficient of y in the second equation.
(5x -2y) -2(2x -y) = (2) -2(-46)
x = 94 . . . . . . simplified
2(94) -y = -46 . . . . substitute into the second equation
y = 2(94) +46 = 234
The solution by elimination is (x, y) = (94, 234).
_____
Additional comment
Here, I like the substitution best, because once we solve for y, we can use that with our solution for x. It seems like less work than using the elimination method, though both solutions are shown here in 4 lines.