Question

How many solutions does the system of equations below have? 6x − 10y = 3 12x − 20y = 6

a) No solution
b) One solution
c) Infinite solutions
d) Cannot be determined

Answer 1

The system of equations has infinite solutions.

Step-by-step explanation:

To determine how many solutions the system of equations has, we can solve the equations and see if there is a unique solution, no solution, or infinitely many solutions.

First, we can simplify the second equation by dividing both sides by 2: 6x - 10y = 3 (1)

Now, we can see that equation (1) is the same as the first equation, which means the two equations represent the same line. Therefore, the system of equations has infinite solutions (c).