How do you solve the following linear system: #3x + 2y = –5 , x-2y=13 #?

1 Answer
May 21, 2018

Answer:

See a solution process below:

Explanation:

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

#x - 2y = 13#

#x - 2y + color(red)(2y) = 13 + color(red)(2y)#

#x - 0 = 13 + 2y#

#x = 13 + 2y#

Step 2) Substitute #(13 + 2y)# for #x# in the first equation and solve for #y#:

#3x + 2y = -5# becomes:

#3(13 + 2y) + 2y = -5#

#(3 * 13) + (3 * 2y) + 2y = -5#

#39 + 6y + 2y = -5#

#39 + (6 + 2)y = -5#

#39 + 8y = -5#

#39 - color(red)(39) + 8y = -5 - color(red)(39)#

#0 + 8y = -44#

#8y = -44#

#(8y)/color(red)(8) = -44/color(red)(8)#

#(color(red)(cancel(color(black)(8)))y)/cancel(color(red)(8)) = -(4 xx 11)/color(red)(4 xx 2)#

#y = -11/2#

Step 3) Substitute #-11/2# for #y# in the solution to the second equation at the end of Step 1 and calculate #x#:

#x = 13 + 2y# becomes:

#x = 13 + (2 xx -11/2)#

#x = 13 + (-11)#

#x = 2#

The Solution Is:

#x = 2# and #y = -11/2#

Or

#(2, -11/2)#