Question

Solve the following system of equations for x and y:

1. X - 2y = 5
2. 2x - 4y = 10

Select the correct option:

a) Infinitely many solutions
b) No solutions
c) (0, 0)
d) (5, 10)

Answer 1

The system of equations X - 2y = 5 and 2x - 4y = 10 has infinitely many solutions because the second equation is the first multiplied by 2, indicating they represent the same line.

Step-by-step explanation:

To solve the following system of equations for x and y:

1. X - 2y = 5
2. 2x - 4y = 10

We observe that the second equation is simply the first equation multiplied by 2. This indicates that both equations represent the same line. Thus, they will have infinitely many points of intersection, meaning there are infinitely many solutions to this system. No specific single solution for x and y exists.

By comparing the coefficients, we can see the system is dependent:

• The coefficients of x are in the ratio 1:2 for both equations
• The coefficients of y also have the same 1:2 ratio.
• And crucially, the constants on the right side of the equations also have the same 1:2 ratio.

Therefore, the correct answer is option (a) infinitely many solutions.