Question

Solve the system. Explain your choice of solution method.
3 x minus 2 y
equals
negative 13
2 x minus 4 y
equals
negative 30
Question content area bottom
Part 1
Explain your choice of solution method.
A.
The substitution method is the best choice because both of the equations are already solved for constants.
B.
The substitution method is the best choice because one of the variables in one equation has a coefficient of 1.
C.
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.
D.
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.
E.
The substitution method is the best choice because one of the equations is already solved for the variable.

Answer 1

First, pick method: C. The elimination method is best because the coefficient of y in the second equation (-4) is a multiple of the coefficient of y in the first equation (-2).

Solve by elimination:
Multiply the first equation by 2:
6x - 4y = -26
Second equation:
2x - 4y = -30

Subtract the second from the first:
(6x - 4y) - (2x - 4y) = -26 - (-30) → 4x = 4 → x = 1

Substitute x = 1 into 3x - 2y = -13:
3(1) - 2y = -13 → 3 - 2y = -13 → -2y = -16 → y = 8

Solution: (x, y) = (1, 8).