how many solutions does x - 2y = 6 3x - 6y = 18 have

Answer 1

To determine the number of solutions, we can analyze the system of equations by manipulating the given equations.

First, let's rewrite the first equation as follows:

x - 2y = 6
x = 6 + 2y

Substituting the value of x in the second equation, we have:

3(6 + 2y) - 6y = 18
18 + 6y - 6y = 18
18 = 18

From this, we see that the equation is true for any value of y.

Therefore, the system of equations is dependent, which means that the two equations represent the same line. This implies that there are infinitely many solutions for the system of equations.