Solving a 2×2 System with Cramer's Rule

Algebra 2 · Axiom Academy

EXAMPLE Solving with Cramer's Rule Find x and y using three determinants — no substitution or elimination required. Use Cramer's Rule to solve the system 2x+3y=13 and x-2y=-4 for x and y . Nice work! You've used Cramer's Rule to solve a 2 ×︎ 2 system. Remember: Cramer's Rule needs : the main determinant must be nonzero for a unique solution. Three determinants: D (the coefficients), D_x ( x -column replaced by the constants), and D_y ( y -column replaced). Formula: x = D_x/D and y = D_y/D — divide each variable's determinant by the main determinant. Always verify: substitute your solution back into both original equations. Cramer's Rule gives a direct, formulaic path to the solution whenever .

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