Question

4x -2y =6
7x -5y=3

please solve this by substitution method.​

Answer 1

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

$4x - 2y = 6...(i)$

$7x - 5y = 3...(ii)$

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

The values of $x$ and $y$ by substitution method.

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

:⟼  $4x - 2y = 6$

:⟼  $4x = 6 + 2y$

:⟼  $x = \frac{6 + 2y}{4} ...(iii)$

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

:⟼  $7( \frac{6 + 2y}{4} )- 5y = 3$

:⟼  $\frac{42 + 14y}{4} - \frac{5y \times 4}{1 \times 4} = 3$

:⟼  $\frac{42 + 14y - 20y}{4} = 3$

:⟼  $- 6y = 12 - 42$

:⟼  $y = \frac{ - 30}{ - 6}$

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

Plugging the value of $y$ in $eqn.(i)$ gives us

:⟼  $4x - 2 \times 5 = 6$

:⟼  $4x = 6 + 10$

:⟼  $x = \frac{16}{4}$

:⟼ $\bigstar \: \boxed{\sf{\color{red}{x=4}}}$

Therefore, the values of $x$ and $y$ are $\boxed{ 4 }$ and $\boxed{ 5 }$ respectively.