Question

Which system of equations is equivalent to the system of equations shown?

x - 6y = 3
4x - 8y = 4

A) 5x - 14y = 7 and 2x - 12y = 6
B) 5x + 14y = 7 and 2x - 12y = -6
C) 5x - 14y = 7 and 2x + 12y = 6
D) 5x - 14y = 7 and 2x - 12y = -6

Please provide an explanation of how you arrived at your answer.

Answer 1

The equivalent system of equations is 5x - 14y = 7 and 2x - 12y = -6, which corresponds to option D.

Step-by-step explanation:

To find the system of equations that is equivalent to the given system, we can perform some algebraic manipulations. First, let's simplify the given system by dividing both equations by their respective coefficients of x. This gives us:

x - 6y = 3 becomes 1/4x - (6/4)y = 3/4 or (1/4)x - (3/2)y = 3/4

4x - 8y = 4 becomes 4x/4 - (8/4)y = 4/4 or 1x - 2y = 1

Combining these equations, we have:

(1/4)x - (3/2)y = 3/4 and 1x - 2y = 1

The equivalent system of equations is therefore 5x - 14y = 7 and 2x - 12y = -6, which corresponds to option D.