418,077 views
42 votes
42 votes
Solve the system. Explain your choice of solution method.

5x - 2y = 2
2x - y = - 46
Explain your choice of solution method.
O A. The substitution method is the best choice because one of the equations is already solved for the variable.
OB. The substitution method is the best choice because one of the variables in one equation has a coefficient of 1
O C. The elimination method is the best choice because the coefficient of x in the second equation is a multiple of the coefficient of x in the first equation
OD. The substitution method is the best choice because both of the equations are already solved for constants
O E. The elimination method is the best choice because the coefficient of y in the second equation is a multiple of the coefficient of y in the first equation

User Broo
by
2.7k points

1 Answer

13 votes
13 votes

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.

Solve the system. Explain your choice of solution method. 5x - 2y = 2 2x - y = - 46 Explain-example-1
User YBathia
by
2.9k points