How do you solve the following system: #7y - 2x = 10, -5x − y = 14 #?

1 Answer
Jan 28, 2016

Answer:

#y = 22/37# and #x = #-108/37#

Explanation:

Let's solve the second equation for y, which should be simply since it doesn't have a coefficient. It starts off as:

#-5x -y = 14#

Add y to both sides and subtract 14 from both sides:

#-5x - 14 = y#, or in reverse: #y = -5x - 14#.

Now we can plug that into the second equation:

#7(-5x - 14) - 2x = 10#

Multiply through: (tip: #7 * 14# is #98#)
#-35x - 98 - 2x = 10#

Consolidate #x#'s:
#-37x - 98 = 10#

Add #98# to both sides:
#-37x = 108#

Divide by #-37#:
#x = 108/-37#

Now plug that back into the initial equation:
#-5 * 108/-37 - y = 14#
#540/37 - y = 14#

Add #y# and subtract #14#:
#540/37 - 14 = y#

Get a common denominator for #14#:
#540/37 - 518/37 = y#

Subtract:
#22/37 = y#