Question

Solve the following simultaneous equations :

83x – 67y = 383

67x – 83y = 367.

Answer 1

write all step clearly

Answer 2

• Given equations,

             83x - 67y = 383 -----------------(1)

             67x - 83y = 367 -----------------(2)

• Making coefficients of x in both equations equal.

• Multiply equation (1) with 67

        (1)x67 ⇒ 5561x - 4489y = 25661  ------------(3)

• Multiply equation (2) with 83

        (2)x83 ⇒ 5561x - 6889y = 30461 ------------(4)

• Now, subtracting (4) from (3)

        5561x - 4489y = 25661

        5561x - 6889y = 30461

           0x    + 2400y = -4800

              y = $\frac{-4800}{2400}$ = - 2

• Substituting y in (1)

         83x - 67(-2) = 383

         83x + 134 = 383

         83x = 383 - 134

         83x = 249

           x = $\frac{249}{83}$ = 3

• Therefore, solution of given simultaneous equations is    

             x = 3, y = - 2