How do you solve the following system?: # 3x + y = -1 , 2x – y = -4 #

1 Answer
May 28, 2018

Answer:

See a solution process below:

Explanation:

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

#3x + y = -1#

#3x - color(red)(3x) + y = -1 - color(red)(3x)#

#0 + y = -1 - 3x#

#y = -1 - 3x#

Step 2) Substitute #(-1 - 3x)# for #y# in the second equation and solve for #x#:

#2x - y = -4# becomes:

#2x - (-1 - 3x) = -4#

#2x + 1 + 3x = -4#

#2x + 3x + 1 = -4#

#(2 + 3)x + 1 = -4#

#5x + 1 = -4#

#5x + 1 - color(red)(1) = -4 - color(red)(1)#

#5x + 0 = -5#

#5x = -5#

#(5x)/color(red)(5) = -5/color(red)(5)#

#(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = -1#

#x = -1#

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

#y = -1 - 3x# becomes:

#y = -1 - (3 xx -1)#

#y = -1 - (-3)#

#y = -1 + 3#

#y = 2#

The Solution Is:

#x = -1# and #y = 2#

Or

#(-1, 2)#