System of Equations Solver — 2-Variable Linear System
Solve systems of two linear equations using the Cramer Rule determinant method. Get step-by-step solutions for unique, infinite, or no solution cases.
System Solver
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Determinant (D)
▲ -19
Solution Type
▲ Unique solution
Step-by-Step Work
System of equations: 2x + 3y = 7 5x + -2y = 3 Determinant D = a₁·b₂ − a₂·b₁ = 2·-2 − 5·3 = -19 Dx = c₁·b₂ − c₂·b₁ = 7·-2 − 3·3 = -23 Dy = a₁·c₂ − a₂·c₁ = 2·3 − 5·7 = -29 D = -19 ≠ 0 → unique solution x = Dx / D = -23 / -19 = 1.210526 y = Dy / D = -29 / -19 = 1.526316
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Linear System — Two Lines
Determinant (D)
-19
Solution
(1.210526, 1.526316)
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