Question

.Given: 3x–5y=4; 9x=2y+7. Solve above equations by Elimination method and find the value of x

Answer 1

Solution :

$\bigstar$ By Elimination Method :

$\sf{3x-5y=4}\\\bullet\sf{3x-5y-4=0......................(1)}$

&

$\sf{9x=2y+7}\\\bullet\sf{9x-2y-7=0......................(2)}$

We can multiplying by 2 in equation (1),we get;

$\mapsto\sf{2(3x-5y-4=0)}\\\\\mapsto\sf{6x-10y-8=0......................(3)}$

We can multiplying by 5 in equation (2),we get;

$\mapsto\sf{5(9x-2y-7=0)}\\\\\mapsto\sf{45x-10y-35=0....................(4)}$

Subtracting equation (3) & equation (4), we get;

$\mapsto\sf{6x-45x-10y-(-10y)-8-(-35)=0}\\\\\mapsto\sf{-39x\cancel{-10y+10y} -8+35=0}\\\\\mapsto\sf{-39x+27=0}\\\\\mapsto\sf{-39x=-27}\\\\\mapsto\sf{x=\cancel{\dfrac{-27}{-39} }}\\\\\mapsto\bf{x=9/13}$

∴ Putting the value of x in equation (1), we get;

$\mapsto\sf{3\bigg(\dfrac{9}{13} \bigg)-5y-4=0}\\\\\\\mapsto\sf{\dfrac{27}{13} -5y-4=0}\\\\\\\mapsto\sf{27-65y-52=0}\\\\\mapsto\sf{-65y-25=0}\\\\\mapsto\sf{-65y=25}\\\\\mapsto\sf{y=\cancel{25/-65}}\\\\\mapsto\bf{y=-5/13}$

Thus;

The value of x will be 9/13 .