Question

1. 3x + 2y = 11; 2x + 3y = 4​

Answer 1

Step-by-step explanation:

Given that:

3x+2y=11, (1)

On multiplying by 3, we get

9x+6y=33 (2)

2x+3y=4, (3)

On multiplying by 2, we get

4x+6y=8 (4)

On subtracting equation (4) from equation (2), we get

5x=25,

x=5

Substituting in equation (1), we get

15+2y=11

y=−2

Answer 2

Answer

${\sf \dashrightarrow 3x + 2y = 11 \: \: --- (i)}$

${\sf \dashrightarrow 2x + 3y = 4 \: \: --- (ii)}$

By taking equation (i),

${\sf \dashrightarrow 3x + 2y = 11}$

${\sf \dashrightarrow 3x = 11 - 2y}$

${\sf \dashrightarrow x = \dfrac{11 - 2y}{3}}$

Now, substitute the value of x in equation (ii)

${\sf \dashrightarrow 2x + 3y = 4}$

${\sf \dashrightarrow 2 \bigg( \dfrac{11 - 2y}{3} \bigg) + 3y = 4}$

${\sf \dashrightarrow \dfrac{22 - 4y}{3} + 3y = 4}$

${\sf \dashrightarrow \dfrac{22 - 4y + 9y}{3} = 4}$

$\sf \dashrightarrow 22 - 4y + 9y = 3 \times 4$

${\sf \dashrightarrow 22 + 5y = 12}$

${\sf \dashrightarrow 5y = 12 - 22}$

${\sf \dashrightarrow 5y = 10}$

${\sf \dashrightarrow y = \dfrac{10}{5}}$

${\sf \dashrightarrow y = 5}$

Now, substitute the value of y in equation (i)

${\sf \dashrightarrow 3x + 2y = 11}$

${\sf \dashrightarrow 3x + 2(5) = 11}$

${\sf \dashrightarrow 3x + 10 = 11}$

${\sf \dashrightarrow 3x = 11 - 10}$

${\sf \dashrightarrow 3x = 1}$

${\sf \dashrightarrow x = \dfrac{1}{3}}$

Thus, Value of x and y are 1/3 and 5 respectively.