Question

solve the equation:2x-3y=9; 2x+y=13​

Answer 1

$\bf{\underline{Given}}$

Equation:-

$\sf{2x-3y = 9}$

$\sf{2x+y = 13}$

$\bf{\underline{Method\:used}}$

Substitution Method.

Solution:-

$\sf{2x-3y = 9 \longrightarrow (i)}$

$\sf{2x+y = 13 \longrightarrow (ii)}$

$\sf{\underline{From\:eq.(i)}}$

$\sf{2x-3y = 9}$

= $\sf{2x = 9+3y}$

$\sf{\implies x = \dfrac{9+3y}{2}}$

$\sf{\underline{Substituting\:the\:value\:of\:x\:in\:eq.(ii)}}$

$\sf{2x+y = 13}$

= $\sf{2\times\bigg(\dfrac{9+3y}{2}\bigg) + y = 13}$

$\sf{\implies 9+3y+y = 13}$

$\sf{\implies 9+4y = 13}$

$\sf{\implies 4y = 13-9}$

$\sf{\implies 4y = 4}$

$\sf{\implies y = \dfrac{4}{4}}$

$\sf{\implies y = 1}$

$\sf{\underline{Putting\:the\:value\:of\:y\:in\:eq.(i)}}$

$\sf{2x-3y = 9}$

= $\sf{2x - 3\times1 = 9}$

$\sf{\implies 2x - 3 = 9}$

$\sf{\implies 2x = 9+3}$

$\sf{\implies 2x = 12}$

$\sf{\implies x = \dfrac{12}{2}}$

$\sf{\implies x = 6}$

$\sf{\underline{Therefore}}$

x = 6

y = 1

$\bf{\underline{Verification}}$

$\sf{2x - 3y = 9}$

= $\sf{2\times6 - 3\times1 = 9}$

= $\sf{12-3=9}$

= $\sf{9=9}$ [Verified]

$\sf{2x + y = 13}$

= $\sf{2\times6 + 1 = 13}$

= $\sf{12+1=13}$

= $\sf{13=13}$ [Verified]