How do you solve the following system?: #5x -7y =-43 , -13x +y = 8#

1 Answer
Jun 3, 2017

Answer:

See a solution process below:

Explanation:

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

#-13x + y = 8#

#color(red)(13x) - 13x + y = color(red)(13x) + 8#

#0 + y = 13x + 8#

#y = 13x + 8#

Step 2) Substitute #(13x + 8)# for #y# in the first equation and solve for #x#:

#5x - 7y = -43# becomes:

#5x - 7(13x + 8) = -43#

#5x - (7 * 13x) - (7 * 8) = -43#

#5x - 91x - 56 = -43#

#(5 - 91)x - 56 = -43#

#-86x - 56 = -43#

#-86x - 56 + color(red)(56) = -43 + color(red)(56)#

#-86x - 0 = 13#

#-86x = 13#

#(-86x)/color(red)(-86) = 13/color(red)(-86)#

#(color(red)(cancel(color(black)(-86)))x)/cancel(color(red)(-86)) = -13/86#

#x = -13/86#

Step 3) Substitute #-13/86# for #x# in the solution to the second equation at the end of Step 1 and calculate #y#;

#y = 13x + 8# becomes:

#y = (13 * -13/86) + 8#

#y = -169/86 + 8#

#y = -169/86 + (86/86 xx 8)#

#y = -169/86 + 688/86#

#y = 519/86#

The solution is: #x = -13/86# and #y = 519/86# or #(-13/86, 519/86)#