Question

Solve

41x + 53y = 135

53x + 41y = 147

• A. x = 1 and y = 1
• B. x = 2 and y = 1
• C. x = 2 and y = 2
• D. x = -2 and y = -1

Answer 1

The correct option is B

x = 2 and y = 1

Given equations : 41x + 53y = 135 and 53x + 41y = 147

Here the coefficient of x in the first equation is equal to the coefficient of y in the second equation and the coefficient of y in the first equation is equal to the coefficient of x in the second equation.

Adding the two given equations we get

94x + 94y = 282 $\Rightarrow$ x + y = 3.......(i)

Subtracting the two given equations we get

-12x + 12y = -12 $\Rightarrow$ -x + y = -1.......(ii)

Now solving (i) and (ii) we get

x = 2 and y = 1