Question

Solve the equations `2a-3b=-5`, `4a+3b=17` and `5c-2a=1`?

Answer 1

`a=2`, `b=3` and `c=1`

Explanation:

`2a-3b=-5` ....................................(A)
`4a+3b=17` ....................................(B)
`5c-2a=1` ....................................(C)

Adding (A) and (B), we get `2a-3b+4a+3b=-5+17`

i.e. `6a=12` i.e. `a=12/6=2`

Putting this in (B), we get `4xx2+3b=17`

or `8+3b=17` i.e. `3b=17=8=9` and `b=9/3=3`

and putting value of `a` in (C), we get

`5c-2xx2=1`

or `5c-4=1` i.e. `5c=1+4=5` i.e. `c=1`

and `a=2`, `b=3` and `c=1`

Answer 2

`a=2,b=3,c=1`

Explanation:

If we add the first 2 equations, we will eliminate b and be able to solve for a

`2a-3b=-5color(white)(xxx)to(1)`
`4a+3b=color(white)(xx)17color(white)(xx) to(2)`
`"---------------------"`
`6a+0color(white)(x)=color(white)(xx)12rArra=2`

Substitute a = 2 into (2)

`(4xx2)+3b=17rArr8+3b=17`

`rArr3b=17-8=9rArrb=3`

Substitute a = 2 into the third equation and solve for c

`rArr5c-(2xx2)=1rArr5c-4=1`

`rArr5c=1+4=5rArrc=1`

`"Thus " a=2,b=3" and " c=1`