# What are the possibe cases in a geometrice sense of a lineary system in two variables.

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Since the equations of system are linear equations, they are represented by lines.

There are two possible cases such that:

1) the solution to the system is unique and it represents the point of intersection of the lines representing the equations of the system.

You may consider the following system of linear equations, in two variables, as an example to the first case discussed such that:

2x+y=1

x-y = 2

Adding the equations yields:

3x = 3 => x = 1

1 - y = 2 => -y = 1 => y = -1

Hence, the solution to the system (1,-1) is the point of intersection of lines 2x+y=1 and x-y = 2 such that:

2) the system has no solution, hence, the line are not intercept each other, the lines are parallel.

y=3x-5

y = 3x + 2