Solve by the elimination method

Question

7a+6b=23

-7a+b=12

Determine the solution of the system. Select the correct choice below and if necessary write the answer out in a ordered pair.

Or is there infinitely many solutions

Or is there no solution at all?

 

Answer 1

First  Combine these equations. This will eliminate the a term.

7a+6b=23

-7a+b=12

      7b=35

if 7b=35

then b=5

put 5 for b in the original equation

7a+6(5)=23

7a+30=23

7a=-7

a=-1

check:

7(-1)+6(5)=23

-7+30=23

23=23