Linear Combination Calculator

Your details

System mode solves two equations for x and y. Vector mode computes a scalar1*v1 + scalar2*v2 for 2D or 3D vectors.
The number multiplying x in the first equation.
The number multiplying y in the first equation.
The right-hand side of the first equation.
The number multiplying x in the second equation.
The number multiplying y in the second equation.
The right-hand side of the second equation.
x
29/17

Value of the variable x solving the system

y26/17
Solution typeUnique solution
Determinant-17
Determinant-17

Solution: x = 29/17, y = 26/17

  • Substituting back: the values satisfy both original equations exactly.
  • The determinant of the coefficient matrix is -17, which is non-zero, confirming a unique intersection point.
  • The elimination method works by scaling equations so that adding or subtracting them cancels one variable, leaving a single equation in one unknown.

Next stepAlways verify your answer by substituting x and y back into both original equations to confirm the left-hand side equals the right-hand side.

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