Step 1) Solve the second equation for #y#:
#6x + 2y = -4#
#-color(red)(6x) + 6x + 2y = -color(red)(6x) - 4#
#0 + 2y = -6x - 4#
#2y = -6x - 4#
#(2y)/color(red)(2) = (-6x - 4)/color(red)(2)#
#(color(red)(cancel(color(black)(2)))y)/cancel(color(red)(2)) = (-6x)/color(red)(2) - 4/color(red)(2)#
#y = -3x - 2#
Step 2) Substitute #(-3x - 2)# for #y# in the first equation and solve for #x#:
#5x + 8y = -2# becomes:
#5x + 8(-3x - 2) = -2#
#5x + (8 * -3x) - (8 * 2) = -2#
#5x - 24x - 16 = -2#
#(5 - 24)x - 16 = -2#
#-19x - 16 = -2#
#-19x - 16 + color(red)(16) = -2 + color(red)(16)#
#-19x - 0 = 14#
#-19x = 14#
#(-19x)/color(red)(-19) = 14/color(red)(-19)#
#(color(red)(cancel(color(black)(-19)))x)/cancel(color(red)(-19)) = -14/19#
#x = -14/19#
Step 3) Substitute #-14/19# for #x# in the solution to the second equation at the end of Step 1 and calculate #y#:
#y = -3x - 2# becomes:
#y = (-3 xx -14/19) - 2#
#y = 42/19 - 2#
#y = 42/19 - (19/19 * 2)#
#y = 42/19 - 38/19#
#y = 4/19#
The Solution Is: #x = -14/19# and #y = 4/19# or #(-14/19, 4/19)#
