Question

2ax+3by=a+2b, 3ax+2by=2a+b​

Answer 1

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; simplifying

y = (4b -a)/5b……(6)

Adding (3) and (5)

10ax = 8a -2b; simplifying

x= (4a - b)/5a….(7)

Check

Is 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 side

Proves

x= (4a - b)/5a and y = (4b -a)/5b are correct.

So, l hope you it's help you