Question

What is the solution to the system of linear equations represented by the matrix below?

[2 4] [x] = [6]
[1 2] [y] =[3]
A. x= 3 , y= 0
B. x= 0 , y= 3/2
C. The system of equations has no solution
D. The system of equations has infinite solutions

Answer 1

The solution to the system of linear equations represented by the given matrix is that the system has an infinite number of solutions.

Step-by-step explanation:

To find the solution to the system of linear equations represented by the given matrix, we can use matrix operations. We need to transform the matrix equation into simplified form by applying row operations.

1. First, we can multiply the first row of the matrix by 1/2, which gives us: [1 2] [x] = [3]
2. Then, we can subtract 2 times the first row from the second row of the matrix, which gives us: [1 2] [x] = [3] and [0 0] [y] = [0]

Since the second row represents the equation 0y = 0, it means that y can be any value. However, the first row represents the equation x + 2y = 3. By rearranging this equation, we can solve for x, which gives us x = 3 - 2y. Therefore, the system of equations has an infinite number of solutions, and the correct answer is D. The system of equations has infinite solutions.