Question

by Cramer rule please tell the answer

Answer 1

The answer is given below :

RULE :

Let us consider two equations -

a1 x + b1 y = c1
a2 x + b2 y = c2

Then, the required solution be

x = (b2 c1 - b1 c2)/(a1 b2 - a2 b1)

and

y = (a1 c2 - a2 c1)/(a1 b2 - a2 b1)

SOLUTION :

The given equations are

x + 3y = 45 .....(i)
3x + 4y = 65 .....(ii)

So, the required solution by Cramer's Rule be

x = (45×4 - 65×3)/(1×4 - 3×3)

= (180 - 195)/(4 - 9)

= (-15)/(-5)

= 3

and

y = (1×65 - 3×45)/(1×4 - 3×3)

= (65 - 135)/(4 - 9)

= (-70)/(-5)

= 14

Therefore, the required solution be

x = 3 and y = 14.

VERIFICATION :

When x = 3, y = 14,

L.H.S. of (i)
= 3 + 3×14
= 3 + 42
= 45
= R.H.S. of (i)

and

L.H.S. of (ii)
= 3×3 + 4×14
= 9 + 56
= 65
= R.H.S. of (ii)

So, the values of x and y are verified.

Thank you for your question.