How do you find 'x' and 'y' if (2ax+3by=a+2b ; 3ax+2by=2a+b)?Register on Spartan Poker & win exciting prizes!2ax + 3by = a+2b….(1)3ax + 2by = 2a+b….(2)Adding (1) and (2)5AX + 5by = 3a + 3b….(3)Subtracting (1) from (2)AX - by = a-b …………..(4)so 5ax - 5by = 5a - 5b….(5)Subtracting (5) from (3)10by = 8b -2a; simplifyingy = (4b -a)/5b……(6)Adding (3) and (5)10ax = 8a -2b; simplifyingx= (4a - b)/5a….(7)CheckIs 2ax + 3by = a+2b….(1)?Left hand side ..Substitute valueof x from eqn.…(7) and y from eqn.…(6)2a* [(4a - b)/5a] + 3b*[(4b -a)/5b]= [8a - 2b + 12b - 3a]/5 = [5a - 10b ]/5 = a + 2b i.e. Right hand sideProvesx= (4a - b)/5a and y = (4b -a)/5b are correct.Don’t MISS vaccination. Lockdown diseases, not childhood.We can use 3 methods to solve these equationsSubstitution methodElimination methodCross multiplication METHODI am using elimination methodLet2ax+3by=a+2b…………(1)3ax+2by=2a+b…………(2)On multiplying(1) by 3 and(2)by 26ax+9by=3a+6b……….(3)6ax+4by=4a+2b………..(4)(3)-(4)(6ax-6ax)+(9by-4by)=(3a-4a)+(6b-2b)5by=-a+4by=(4b-a)/5b putting in equation(1)2ax+3b(4b-a)/5b=a+2b2ax=a+2b-(12b^2-3ab)/5b2ax=(5ab+10b^2–12b^2+3ab)/5b2ax=(8ab-2b^2)/5bx=(4a-b)/5aNow verifyPutting the value of x and y in equation(1)LHS2a(4a-b)/5a+3b(4b-a)/5b=(8a-2b+12b-3a)/5=(5a+10b)/5=a+2b =RHS...2ax+3by=a+2b ….(1)3ax+2by=2a+b …..(2)(2) - (1) givesax - by = a - bImplies 5ax - 5by = 5a - 5b …..(3)(1)+(2)=>5ax + 5by = 3a + 3b …..(4)(3)+(4)=> 10ax = 8a - 2b = 2(4a - b)So x = (1/5a)(4a-b)(4) -(3) gives 10by= -2a + 8b = 2(4b - a)So y= (1/5b)(4b - a)