Question

Find the value of (x-y), if
3x+4y=11;4x+3y=10​

Answer 1

Answer:

$-1$

Step-by-step explanation:

The given equations are: $3x + 4y = 11$      --$(1)$

                                          $4x + 3y = 10$      --$(2)$

We have to find $(x-y)$

First, lets solve $(1)$ and $(2)$

⇒ in $(1)$

   $3x + 4y = 11$

⇒ $3x = 11-4y$

⇒ $x = \frac{11-4y}{3}$

   Substituting the value of $x$ in $(2)$

⇒ $4(\frac{11-4y}{3}) + 3y = 10$

⇒ $\frac{44-16y}{3} + 3y = 10$

⇒ $\frac{44 -16y + 9y}{3}=10$

⇒ $\frac{44-7y}{3} = 10$

⇒ $44-7y = 30$

⇒ $-7y = 30-44$

⇒ $-7y = -14$

⇒ $y = 2$

   Substituting the value of $y$ in $(1)$

⇒ $3x + 4(2) = 11$

⇒ $3x+8 = 11$

⇒ $3x = 11-8$

⇒ $3x = 3$

⇒ $x = 1$

⇒ Solution of $(1)$ and $(2)$ is $x = 1$ and $y = 2$

⇒ $x-y = 1-2 = -1$

Answer 2

Answer

$\sf \dashrightarrow 3x + 4y = 11 \: \: --- (i)$

$\sf \dashrightarrow 4x + 3y = 10 \: \: --- (ii)$

First, we should find the values of x and y.

By first equation,

$\sf \dashrightarrow 3x + 4y = 11$

$\sf \dashrightarrow 3x = 11 - 4y$

$\sf \dashrightarrow x = \dfrac{11 - 4y}{3}$

Now, we can find the value of y by second equation.

$\sf \dashrightarrow 4x + 3y = 10$

$\sf \dashrightarrow 4 \bigg( \dfrac{11 - 4y}{3} \bigg) + 3y = 10$

$\sf \dashrightarrow \dfrac{44 - 16y}{3} + 3y = 10$

$\sf \dashrightarrow \dfrac{44 - 16y + 9y}{3} = 10$

$\sf \dashrightarrow \dfrac{44 - 7y}{3} = 10$

$\sf \dashrightarrow 44 - 7y = 10 \times 3$

$\sf \dashrightarrow 44 - 7y = 30$

$\sf \dashrightarrow -7y = 30 - 44$

$\sf \dashrightarrow -7y = -14$

$\sf \dashrightarrow y = \dfrac{-14}{-7}$

$\sf \dashrightarrow y = 2$

Now, we can find the value of x by first equation.

$\sf \dashrightarrow 3x + 4y = 11$

$\sf \dashrightarrow 3x + 4(2) = 11$

$\sf \dashrightarrow 3x + 8 = 11$

$\sf \dashrightarrow 3x = 11 - 8$

$\sf \dashrightarrow 3x = 3$

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

$\sf \dashrightarrow x = 1$

Now, we can find the answer of this question.

$\sf \dashrightarrow x - y$

$\sf \dashrightarrow 1 - 2$

$\sf \dashrightarrow -1$

Hence, the value of (x - y) is -1.