Question

By solving a pair of linear equation x+y=8and 2y-x=1 the value of x and y

Answer 1

Answer:

Let 2y−x=8...(1)

and 3x−y=1...(2)

Multiply (1) by 3, we get

⇒−3x+6y=24...(3)

Subtract (2) by (3), we get

⇒5y=25

⇒y=525=5

Sustitute the value of y=5 in (2)

⇒3x−5=1

⇒3x=6

⇒x=36=2 

Answer 2

$\large\bold{\underline{\underline{Given:-}}}$

$x + y = 8...(i)$

$2y - x = 1...(ii)$

$\large\bold{\underline{\underline{To\:find:-}}}$

The values of $x$ and $y$.

$\large\bold{\underline{\underline{Solution:-}}}$

Let us solve this by substitution method.

From $eqn.\:(i)$, we have

:⟼  $x + y = 8$

:⟼  $x = 8 - y...(iii)$

Substituting $eqn.\:(iii)$ in $(ii)$, we have

:⟼  $2y - (8 - y) = 1$

:⟼  $2y - 8 + y = 1$

:⟼  $2y + y = 1+ 8$

:⟼  $3y = 9$

:⟼  $y = \frac{9}{3}$

:⟼  $\bigstar \: \boxed{\sf{\color{red}{y=3}}}$

Now that we have the value of $y$, let us plug it in $eqn.\:(i)$.

:⟼  $x + 3 = 8$

:⟼  $x = 8 - 3$

:⟼  $\bigstar \: \boxed{\sf{\color{red}{x=5}}}$

Therefore, the values of $x$ and $y$ are $\boxed{ 5 }$ and $\boxed{ 3 }$ respectively.