Question

2y - 4x = 6

y = 2x + 3
A) The system has no solution
B) The system has a unique solution at (0, 3)
C) The system has a unique solution at (1, 5)
D) The system has infinitely many solutions

Answer 1

Upon substituting the second equation into the first and simplifying, we discover that the equations represent the same line, which means the system of equations has infinitely many solutions.

Step-by-step explanation:

To determine whether the system of equations has a solution and what kind of solution it might be, we can analyze the system given:

• 2y - 4x = 6
• y = 2x + 3

Let's substitute the second equation into the first to find the solution:

1. Replace y in the first equation with the expression from the second equation: 2(2x + 3) - 4x = 6.
2. Simplify the equation: 4x + 6 - 4x = 6.
3. Notice that the terms containing x cancel each other out, leaving us with 6 = 6, which is a true statement.
4. Since we ended up with a true statement, it indicates that both equations represent the same line. Therefore, there are infinitely many solutions to the system.

So the correct answer is: The system has infinitely many solutions.