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Determine the number of solutions for the system of equations: $2x + 3y = 6$ and $4x + 6y = 12$.

For the equations $y = 2x + 1$ and y = -rac{1}{2}x + 4, how many intersection points do they have?

Determine the number of solutions for the system of equations: $3x - y = 5$ and $6x - 2y = 10$.

Given the equations $x + 2y = 4$ and $2x + 4y = 8$, how many solutions exist?

Find the solution type for the equations $y = 3x + 2$ and $y = 3x - 5$. What can you conclude?

How many solutions does the system have: $x - y = 1$ and $y = x + 3$?

Analyze the system: $2x - 3y = 6$ and $6x - 9y = 18$. What can you conclude?

For the equations $y = -x + 1$ and $y = -x - 2$, how many solutions exist?

Determine the number of solutions for the system: $4x + y = 8$ and 2x + rac{1}{2}y = 4.

How many solutions exist for the equations $y = 5x - 3$ and $y = 5x + 2$?