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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 a1x + b1y + c1 = 0 and a2x+b2y+c2 = 0 are any two equations. a1 and a2 are the coefficients of x and b1 and b2 are the coefficients of y and c1 and c2 are the constants. If a1b2 = a2b1, then the equations a1x + b1y + c1 = 0 and a2x+b2y+c2 = 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. |