Question

Solve : 141x + 103y = 217; 103x + 141y = 27
 Solve : 55x + 52y = 217; 52x + 55y = 217

Answer 1

Given:

Two systems of equations,

(I) 141x + 103y = 217; 103x + 141y = 27

 and

(II) 55x + 52y = 217; 52x + 55y = 217

To find:

The solution to given systems of equations.

Solution:

(I)

As given, we have,

141x + 103y = 217 (i)

103x + 141y = 27 (ii)

As we can see, the opposite variables in the above system of equations have the same coefficients. So, we will use the elimination method to solve the given pair of equations.

So,

after adding (i) and (ii), we get,

244x + 244y = 244

On dividing the above equation by 244, we get,

x + y = 1 (iii)

Now,

after subtracting the (i) from (ii), we get

38x - 38y = 190

On dividing the above equation by 38, we get,

x - y = 5 (iv)

Now, after adding (iii) and (iv), we get,

2x = 6

x = 3

Now, on putting the value of x in the equation (iii), we get,

y = -2

Hence, the solution to 141x + 103y = 217; 103x + 141y = 27 is x = 3 and y = -2.

(II)

As given, we have,

55x + 52y = 217 (i)

52x + 55y = 217 (ii)

In the above equations, the opposite variables have the same coefficients. So, here also, we will use the elimination method to solve the pair of equations.

So,

after subtracting the (i) from (ii), we get

3x - 3y = 0

3(x - y) = 0

x - y = 0

x = y

Now, on putting the value of x = y in the equation (iii), we get,

55x + 52x = 217

107x = 217

x = 217/107

x = 2.02

also,

y = 2.02

Hence, the solution to 55x + 52y = 217; 52x + 55y = 217 is x = 2.02 and y = 2.02.