How do you solve the following system: #7y − 6x − 5 = 0, -5x − y = 14 #?

1 Answer
May 30, 2018

Answer:

See a solution process below:

Explanation:

Step 1) Solve the second equation for #y#:

#-5x - y = 14#

#-5x - color(blue)(14) - y + color(red)(y) = 14 - color(blue)(14) + color(red)(y)#

#-5x - 14 - 0 = 0 + y#

#-5x - 14 = y#

#y = -5x - 14#

Step 2) Substitute #(-5x - 14)# for #y# in the first equation and solve for #x#:

#7y - 6x - 5 = 0# becomes:

#7(-5x - 14) - 6x - 5 = 0#

#-(7 xx 5x) - (7 xx 14) - 6x - 5 = 0#

#-35x - 98 - 6x - 5 = 0#

#-35x - 6x - 98 - 5 = 0#

#(-35 - 6)x - 103 = 0#

#-41x - 103 = 0#

#-41x - 103 + color(red)(103) = 0 + color(red)(103)#

#-41x - 0 = 103#

#-41x = 103#

#(-41x)/color(red)(-41) = 103/color(red)(-41)#

#(-color(red)(cancel(color(black)(41)))x)/cancel(color(red)(-41)) = -103/41#

#x = -103/41#

Step 3) Substitute #-103/41# for #x# in the solution to the second equation at the end of Step 1 and calculate #y#:

#y = -5x - 14# becomes:

#y = (-5 xx -103/41) - 14#

#y = 515/41 - (41/41 xx 14)#

#y = 515/41 - 574/41#

#y = -59/41#

The Solution Is:

#x = -103/41# and #y = -59/41#

Or

#(-103/41, -59/41)#