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First, calculate the determinant of the coefficient matrix
D = det = 5*6 - 3*4 = 30 - 12 = 18.
Next, calculate the determinant Dx, replacing first column in the coefficient matrix by the right side vector
Dx = det = -14*6 - 4*6 = -84 - 24 = -108.
Next, calculate the determinant Dy, replacing second column in the coefficient matrix by the right side vector
Dy = det = 5*6 - (-14)*3 = 30 - (-42) = 72.
Now the solution is x = = = -6; y = = = 4.
ANSWER. x = -6, y = 4.
Solved.
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On Cramer's rule for solving 2x2-system of equations, see the lesson
- Solution of the linear system of two equations in two unknowns using determinant
and the lessons
- What is a matrix?
- Determinant of a 2x2-matrix
- HOW TO solve system of linear equations in two unknowns using determinant (Cramer's rule)
- Solving systems of linear equations in two unknowns using the Cramer's rule
in this site.