Question

please solve this problem by reduction method with proper solution

Answer 1

$\huge\green{\bold{HELLO!!!}}$



5x + 2y = 4------( 1 )

7x + 3y = 5------( 2 )

By Substitution method
$\\ from \: eqn \: (1) \\ \\\\5x + 2y = 4 \\ \\ = > 2y = 4 - 5x \\ \\ = > y = \frac{4 - 5x}{2} - - - (3)$

Substitute eqn ( 3) in eqn (2)

$\\ 7x + 3y = 5 \\ \\ = > 7x + 3( \frac{4 - 5x}{2} ) = 5 \\ \\ = > 7x + \frac{12 - 15x}{2} = 5 \\ \\ = > 14x + 12 - 15x = 10 \\ \\ = > - x = 10 - 12 \\ \\ = > - x = - 2 \\ \\ = > x = 2$

From eqn ( 3)

$y = \frac{4 - 5x}{2} \\ \\ = > y = \frac{4 - 5(2)}{2} \\ \\ = > y = \frac{4 - 10}{2} \\ \\ = > y = \frac{ - 6}{2} \\ \\ = > y = - 3$

Therefore the value of x = 2 and y = - 3

$\underline{\bold{Verification}}$

5x + 2y = 4------( 1 )

7x + 3y = 5------( 2 )

Eqn ( 1)

LHS =
$5(2) + 2( - 3) \\ \\ 10 - 6 = 4$

= RHS

Eqn (2)

LHS =
$7(2) + 3( - 3) \\ \\ = > 14 - 9 = 5$

= RHS

Hence, it is verified

$\textbf{Hope it helps!!!}$