x Suppose the system of linear equations has no solution. Which is NOT a possible

Question

value of the constant for the second equation?
6x + 9y = 15
2x + 3y =
x
X
X
X
———
A 5
B 10
C
15
D 20

Answer 1

The possible values for the constant in the second equation can be found by solving the system of equations.

Subtracting 2 times the first equation from the second equation, we have:

(2x + 3y) - 2(6x + 9y) = x - 2(15)
2x + 3y - 12x - 18y = x - 30
-10x - 15y = x - 30
-11x - 15y = -30

In order for the system of equations to have no solution, the lines represented by the equations must be parallel and never intersect. Thus, the slopes of the lines should be equal. The slope of the second equation is (-11/15).

Since the slope of the first equation is (-6/9) = (-2/3), any constant value that results in a different slope for the second equation is not possible.

Looking at the answer choices:
A) 5 -> (-11/15) ≠ (-2/3)
B) 10 -> (-11/15) ≠ (-2/3)
C) 15 -> (-11/15) ≠ (-2/3)
D) 20 -> (-11/15) ≠ (-2/3)

Therefore, none of the given answer choices (A, B, C, or D) are possible values for the constant in the second equation.