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4x +3y = 11 ; 3x + 4y = 10

User RobertL
by
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1 Answer

8 votes

Answer:

x = 2 ; y = 1

Explanation:

GIVEN :-


  • 4x + 3y = 11 (eqn.1)

  • 3x + 4y = 10 (eqn.2)

SOLUTION :-

The easiest way to solve such questions where two linear equations (with two variables) ax + by = c and bx + ay = d are given is :-

1) Add both the equations :-


4x + 3y + 3x + 4y = 11 + 10


=> 7x + 7y = 21

Simplify it further.


7(x + y) = 21


=> x + y = (21)/(7) = 3 ..... eqn.3

2) Substract both the equations :-


4x + 3y - 3x - 4y = 11 - 10


=> x - y = 1 ..... eqn.4

3) Now add eqn.3 and eqn.4 to get the value of 'x' :-


x + y + x - y = 3 + 1


=> 2x = 4


=> x = (4)/(2) = 2

4) Substitute the value of 'x' in either eqn.1 or eqn.2 and solve it to get the value of 'y' ( I'm here substituting it in eqn.1 ) :-


4 * 2 +3y = 11


=> 3y = 11 - 8 = 3


=> y = (3)/(3) = 1

User Jordy Langen
by
9.0k points

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