Solve the following pair of equations by using the elimination method. $x 10 + y 5 + 1 = 15, x 8 + y 6 = 15$

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x = 50 and y = 20

x = 90 and y = 40

x = 80 and y = 30

x = 20 and y = 50

answer is C.

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Detailed Solution

Given pair of linear equations is:

x 10 + y 5 + 1 = 15 x 8 + y 6 = 15 On simplifying we get, 5 x + 10 y = 700. … (i) 3 x + 4 y = 360... (i i)

Now to calculate the values of variable x and y
Multiplying Eq. (i) by 2 and Eq. (ii) by 5

10 x + 20 y = 1400 … (i) 15 x + 20 y = 1800 … (i i)

Subtracting Eq. (ii) from Eq. (i), we get,

− 5 x = 400 ⇒ x = 80

Putting the value of x, in equation (i),

8010 + y 5 + 1 = 15 ⇒ y 5 = 6 ⇒ y = 30

Therefore, the values of variables are

x = 80 and y = 30

.
Hence, option (3) is correct.

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