Determinants · Class 12 · CBSE · Science Mathematics
Using Cramer's rule, solve the system 2x + 3y = 13 and 4x − y = 5.
Practice question from Determinants (Class 12 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.
medium · Subjective · Q-50C51D
Using Cramer's rule, solve the system 2x + 3y = 13 and 4x − y = 5.
Answer: The determinant of the coefficient matrix is D = |2 3; 4 −1| = −14. Also, Dx = |13 3; 5 −1| = −28 and Dy = |2 13; 4 5| = −42. Therefore, x = Dx/D = 2 and y = Dy/D = 3.
Solution
For Cramer's rule, D = |2 3; 4 −1| = −14. Replacing the first and second columns by the constants gives Dx = −28 and Dy = −42, so x = Dx/D = 2 and y = Dy/D = 3.
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