Lines

Determine the number of solutions for the system of equations: $2x + 3y = 6$ and $4x + 6y = 12$. What can you conclude about these lines?

If the lines represented by the equations $y = 2x + 1$ and y = -rac{1}{2}x + 3 intersect, what is the point of intersection?

Given the equations $3x - y = 5$ and $6x - 2y = 10$, determine the nature of the solution.

A chemist is plotting the reaction rate in relation to concentration. If the equations $y = 4x + 2$ and $y = 4x - 3$ are drawn on a graph, how many solutions do they have?

Find the point of intersection for the lines represented by $y = -3x + 2$ and $y = 1/3x - 1$.

For the equations $x + 2y = 4$ and $2x + 4y = 8$, identify what the lines represent.

If two lines have slopes of $m_{1} = 1$ and $m_{2} = -1$ and intersect at point $(a, b)$, what can be said about their solutions?

Consider the following equations: $y = 2x + 5$ and $y = 2x - 3$. What does this imply about the number of solutions?

If the equations $2x - 3y = 6$ and $4x - 6y = 12$ are graphed, what type of solution will they present?

Determine the intersection point of the lines $y = -x + 4$ and $y = 2x - 2$.