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

2 Answers
Jan 19, 2017

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

Jan 19, 2017

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