# Lesson Cramer's Rule

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 Algebra: Matrices, determinant, Cramer rule Solvers Lessons Answers archive Quiz In Depth
 This Lesson (Cramer's Rule) was created by by longjonsilver(2297)  : View Source, ShowAbout longjonsilver: I have a new job in September, teaching How do we solve the 3 equations: x+2y+3z = 14 4x-5y+6z = 32 7x+8y-9z = 50 Well, we can pick one of the variables in one of the equations and then substitute that into the other 2 equations and then solve those two equations simultaneously. A rather long winded algebraic solution. A much better way, is to use the theory of determinants in matrices to help. This is Cramer's Rule. First, rewrite the system of equations in a matrix form: Find the determinant, D, of the matrix : . Then put the column in place of the 1st, 2nd and 3rd columns sequentially, and calculate determinants as follows: , , . Cramer's Rule says: x = Dx/D y = Dy/D z = Dz/D Working these out, gives: D   =   354 Dx = 2652 Dy =   432 Dz =   480 x = 2652/354 = 7.4915257 y =   432/354 = 1.2203389 z =   480/354 = 1.3559322 An important note: surely, this method assumes that determinant D is not equal to zero. This lesson has been accessed 15625 times.