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Maths · Test of consistency and solution of simultaneous linear equations in two or three variables using matrices

Solve for x+(2 a-b) y=2,(a- \) 2b) y=3 \)

Solve for \( \boldsymbol{x}, \boldsymbol{y} \) \( (a+2 b) x+(2 a-b) y=2,(a- \) 2b) \( x+(2 a+b) y=3 \)

  • A. \( x=(5 b-2 a), y=10 a b \)
  • B. \( x=\frac{5 b-2 a}{10 a b}, y=\frac{a+10 b}{10 a b} \)
  • C. \( x=\frac{5 b-2 a}{10 a b}, y=\frac{5 a+10 b}{10 a b} \)
  • D. \( x=\frac{5 b+2 a}{10 a b}, y=\frac{a+10 b}{10 a b} \)

Step-by-step solution

Solving the system using Cramer's rule: determinant D = (a+2b)(2a+b) - (2a-b)(a-2b) = 10ab. D_x = 2(2a+b) - 3(2a-b) = 5b-2a. D_y = 3(a+2b) - 2(a-2b) = a+10b. Then x = D_x/D and y = D_y/D.
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