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# Cramer's Rule 2 x 2

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In this lesson, we will learn how to use Cramer's Rule to solve a linear system in two variables. To perform this operation, we will first place each equation of the system in standard form. Once this is done, we will set up D, which is the determinant of the coefficient matrix, D

_{x}which is the same as D with the column for the coefficients of x replaced with the constants, and D_{y}, which is the same as D with the column for the coefficients of y replaced with the constants. Once these are all set up, we calculate the values and then find x as D_{x}/D, and y as D_{y}/D. When we have a special case scenario, such as a linear system with no solution or a linear system with an infinite number of solutions, we can't use Cramer's rule. Our value for D will end up being zero. At this point, we can stop and use some other method to determine which type of special case system we have.Cramer's Rule 2 x 2:

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