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A system of linear equations is called consistent if it has at least one solution, and it is called inconsistent if it has no solution.
Let a_{1}x + b_{1}y + c_{1} = 0 and a_{2}x+b_{2}y+c_{2} = 0 are any two equations. a_{1} and a_{2} are the coefficients of x and b_{1} and b_{2} are the coefficients of y and c_{1} and c_{2} are the constants. If a_{1}b_{2} = a_{2}b_{1}, then the equations a_{1}x + b_{1}y + c_{1} = 0 and a_{2}x+b_{2}y+c_{2} = 0 are inconsistent equations.
Example: Directions: Solve the linear system graphically and determine whether the system is consistent and independent, inconsistent, consistent and dependent. Also write at least 10 examples of your own. 