How do you solve the following system: #6x+2y=-4, x-5y=-9#?

1 Answer
Jun 22, 2018

Answer:

See a solution process below:

Explanation:

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

#x - 5y = -9#

#x - 5y + color(red)(5y) = -9 + color(red)(5y)#

#x - 0 = -9 + 5y#

#x = -9 + 5y#

Step 2) Substitute #(-9 + 5y)# for #x# in the first equation and solve for #y#:

#6x + 2y = -4# becomes:

#6(-9 + 5y) + 2y = -4#

#(6 xx -9) + (6 xx 5y) + 2y = -4#

#-54 + 30y + 2y = -4#

#-54 + (30 + 2)y = -4#

#-54 + 32y = -4#

#-54 + color(red)(54) + 32y = -4 + color(red)(54)#

#0 + 32y = 50#

#32y = 50#

#(32y)/color(red)(32) = 50/color(red)(32)#

#(color(red)(cancel(color(black)(32)))y)/cancel(color(red)(32)) = 25/16#

#y = 25/16#

Step 3) Substitute #25/16# for #y# in the solution to the second equation at the end of Step 1 and calculate #x#:

#x = -9 + 5y# becomes:

#x = -9 + (5 xx 25/16)#

#x = (16/16 xx -9) + 125/16#

#x = -144/16 + 125/16#

#x = -19/16#

The Solution Is:

#x = -19/16# and #y = 25/16#

Or

#(-19/16, 25/16)#