How do you solve the following linear system: #{(4x + 5y = -3) ,( y = 1/2x - 3/2):} #?

1 Answer
Mar 13, 2018

Answer:

See explanation.

Explanation:

You can solve the equation by replacing #y# in the first equation with #1/2x-3/2# from the second equation:

#{(4x+5(1/2x-3/2)=-3),(y=1/2x-3/2):}#

#{(4x+5/2x-15/2=-3),(y=1/2x-3/2):}#

Now we can calculate #x# from the first equation:

#{(13/2x=-3+15/2),(y=1/2x-3/2):}#

#{(13/2x=9/2),(y=1/2x-3/2):}#

#{(13x=9),(y=1/2x-3/2):}#

#{(x=9/13),(y=9/26-3/2):}#

Last step is to put the calculated value of #x# into the second equation to calculate #y#:

#{(x=9/13),(y=9/26-39/26):}#

#{(x=9/13),(y=-1 2/13):}#