Question

Which statement is true about the equations –3x + 4y = 12 and 1/4x – 1/3y = 1?

A. The system of the equations has exactly one solution at (–8, 3).
B. The system of the equations has exactly one solution at (–4, 3).
C. The system of the equations has no solution; the two lines are parallel.
D. The system of the equations has an infinite number of solutions represented by either equation.

Answer 1

Option C. The system of the equations has no solution; the two lines are parallel.

Explanation:

we have

-3x+4y=12 -----> equation A

(1/4)x-(1/3)y=1 ----> equation B

Multiply equation B by -12 both sides

-12*[(1/4)x-(1/3)y]=1*(-12)

-3x+4y=-12 ----> equation C

Compare equation A and equation C

The lines are parallel , but the y-intercepts are different

therefore

The system has no solution