Q1 of 40 Page 98

Solve each of the following pairs of equations by reducing them to a pair of linear equation.


and


Let = p and = q


10p + 2q = 4 …I


15p – 5q = -2 …II


Multiply Eq. I by 5 and Eq. II by 2


50p + 10q = 20


30p – 10q = -4


80p = 16


p =


substitute value of p in eq. I


10 + 2q = 4


⇒ 2 + 2q = 4


⇒ 2q = 2


⇒ q = 1


But, ⇒ 5 = x + y …III


⇒ 1 = x – y ⇒ y = x – 1


Substitute value of y in eq. III


x + x – 1 = 5


⇒ 2x = 6


⇒ x = 3


∴ y = 3 – 1 = 2


x = 3 and y = 2


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