Solve the given pair of linear equations by elimination method 9x + 10y=29 and 10x + 9y=28.

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x=-1, y=2

x= 2, y=1

x=3, y=5

x= 1, y=2

answer is D.

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Detailed Solution

The given equations are

9 x + 10 y = 29

and

10 x + 9 y = 28

.
Adding the given equations to obtain simplified equations and the using elimination method to solve the linear equations as follows:

⇒ 9 x + 10 y + 10 x + 9 y = 29 + 28 ⇒ 19 x + 19 y = 57 ⇒ x + y = 3 … . (1)

Subtracting the given equations,

⇒ 9 x + 10 y − 10 x − 9 y = 29 − 28 ⇒ − x + y = 1... (2)

Adding equations 1 and 2,

⇒ x + y − x + y = 3 + 1 ⇒ 2 y = 4 ⇒ y = 2

Putting value of y in equation (1) to solve for x,

⇒ x + 2 = 3 ⇒ x = 1

Therefore, the values are x =1 and y =2.
Hence, the correct option is 4.

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