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System of Equations Calculator

Solve any 2×2 linear system — get the solution (x, y), the determinant, slope-intercept forms, a live graph of both lines with their intersection, and full step-by-step working.

System:  a₁x + b₁y = c₁  and  a₂x + b₂y = c₂
a₁ x + b₁ y = c₁
a₂ x + b₂ y = c₂

Enter the coefficients for both equations. Decimals and negatives are fine. In each equation, a and b can't both be 0.

Results

Solution
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Determinant (D = a₁·b₂ − a₂·b₁)
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Equation 1 (slope-intercept)
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Equation 2 (slope-intercept)
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Intersection point
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Graph

Equation 1Equation 2Intersection

Step-by-step (elimination method)