How do you solve #3x + 2y = 16# and #2x + 3y = 14#?

1 Answer
Sep 10, 2016

Answer:

Solution is #x=4# and #y=2#

Explanation:

When we have such linear equations, where we have addition only and coefficients of #x# and #y# reversed (i.e. of the type #ax+by=c# and #bx+ay=d#), we can just add the two equations to get one equation and then subtract one from other to get another, which when simplified become equations of the type #x+y=m# and #x-y=n# and easier to solve,

Here we have #3x+2y=16# and #2x+3y=14#

adding them gives #4x+5y=30# or #x+y=6#

subtracting second from first gives #x-y=2#

Now as #x+y=6# and #x-y=2#, adding them we get #2x=8# or #x=4#.

And #y=6-4=2#

Hence solution is #x=4# and #y=2#