Question

3x+-2y=-6
5x-2y=7
how do i solve this Elimination pls

Answer 1

`x=(13)/(2), y=(51)/(4)`

Explanation:

`We\ are\ given,\\3x-2y=-6\\5x-2y=7\\Considering\ this\ system\ of\ equations,\\Let\ 3x-2y=-6\ be\ E_1\\Let\ 5x-2y=7\ be\ E_2,\\Hence,\\Multiplying\ E2\ with\ -1, we\ get:\\3x-2y=-6\\-1(5x-2y)=7*-1\\Hence,\\3x-2y=-6\\-5x+2y=-7\\Now,\\Lets\ add\ E_1\ and\ E_2\ together\\Hence,\\(3x-2y)+(-5x+2y)=(-6)+(-7)\\Hence,\\3x-2y-5x+2y=-13\\Arranging\ And\ Adding\ Like\ terms,\ we\ have:\\3x-5x-2y+2y=-13\\Hence,\\-2x+0y=-13\\-2x=-13\\x=(-13)/(-2)=(13)/(2)`

`Now,\ we\ can\ substitute\ x=(13)/(2)\ in\ E_1\ or\ E_2,\\But,\\Here,\ we'll\ substitute\ it\ in\ E1,\\Hence,\\Substituting\ x=(13)/(2)\ in\ E1,\ we\ have:\\3*(13)/(2)-2y=-6\\(39)/(2)-2y=-6\\-2y=-6- (39)/(2)\\-2y=(-12-39)/(2)\\-2y=(-51)/(2)\\y=(-51)/(2*-2)=(51)/(4)\\Hence,\\x=(13)/(2), y=(51)/(4)`