Question

# Question 9 (iv) Solve the following pairs of equation 12x−1y=−1,    1x+12y=8,x,y ≠0

Solution

## Given pair of linear equations is 12x−1y=−1and 1x+12y=8,x,y ≠0 Let u=1x and v=1y.  Then the above equations can be rewritten as: u2−v=−1 ⇒u−2v=−2....(iii) and u+v2=8⇒2u+v=16.....iv On, multiplying Eq. (iv) by 2 and then adding with Eq. (iii), we get 4u+2v=32u−2v=−2                 –––––––––––      5u=30 ⇒u=6 Now, put the value of u in Eq. (iv), we get 2×6+v=16 ⇒v=16−12=4 ∴ x=1u=16 and y=1v=14

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