Question

The system of equations below has no solution.

(2/3)x + (5/2)y = 15
4x + 15y = 12
Which equation could represent a linear combination of the system?

A. 3x - 7y = 9
B. 2x - 5y = 5
C. (1/3)x + (5/10)y = 1.5
D. (4/6)x + (15/2)y = 6

Answer 1

Equation D, \((4/6)x + (15/2)y = 6\), is the correct linear combination, obtained by multiplying the first equation in the original system by 6 to match the equation provided in choice D.

Step-by-step explanation:

Identifying the Correct Linear Combination

To determine which equation could represent a linear combination of the system provided, we need to consider how linear combinations can be formed by multiplying each equation by a constant and then adding or subtracting the results.

The original system of equations is:

• \((2/3)x + (5/2)y = 1\)
• \(4x + 15y = 12\)

Looking at the answer choices:

• A. \(3x - 7y = 9\)
• B. \(2x - 5y = 5\)
• C. \((1/3)x + (5/10)y = 1.5\)
• D. \((4/6)x + (15/2)y = 6\)

We notice that equation D is a linear combination of our system. By multiplying the first equation of the system by 6, we obtain equation D:

• \(6 * ((2/3)x + (5/2)y) = 6 * 1\)

This simplifies to:

• \((4/6)x + (15/2)y = 6\)

Which matches the equation provided in choice D.