Question

$3x + 2y = 11 \\ 2x + 3y = 10$

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Answer 1

Answer:

x = 13/5 and y = 8/5

Step-by-step explanation:

3x + 2y =11 ----------(1)

2x + 3y = 10 ------(2)

BY substitution method

from eq 1

3x + 2y = 11

3x = 11 - 2y

x = (11 - 2y)/3

put x in eq 2

2[(11-2y)/3] + 3y = 10

(22 - 4y)/3 + 3y = 10

(22 - 4y + 9y)/3 = 10

22 - 4y + 9y = 10 × 3

22 + 5y = 30

5y = 30 - 22

5y = 8

y = 8/5

put y in eq 1

3x + 2y = 11

3x + 2(8/5) = 11

3x + 16/5 = 11

3x = 11 - 16/5

3x = (55 - 16)/5

3x = 39/5

x = 39/(5 × 3)

x = 13/5

Answer 2

Answer:-

The value of x is 13/5 or 2.6 and the value of y is 8/5 or 1.6 respectively.

Solution:-

3x + 2y = 11 .......(i)

2x + 3y = 10 .......(ii)

Solving the following pair of linear simultaneous equation by the elimination method.

Multiplying eqn.(i) by 2 and eqn.(ii) by 3, we get:-

3x + 2y = 11 } ×2

=> 6x + 4y = 22 .......(iii)

2x + 3y = 10 } ×3

=> 6x + 9y = 30 .......(iv)

By Subtracting eqn.(iii) & eqn.(iv), we get:-

6x + 4y = 22

6x + 9y = 30

- - -

__________________________

-5y = -8

5y = 8

y = 8/5

Hence the value of y is 8/5 or 1.6

Putting the value of x in eqn.(i), we get:-

3x + 2y = 11

=> 3x + 2 × 8/5 = 11

=> 3x + 16/5 = 11

=> 3x = 11 - 16/5

=> 3x = (55 - 16)/5

=> 3x = 39/5

=> x = 39/5 × 3

=> x = 13/5

Hence the value of x is 13/5 or 2.6.