Step 1) Solve each equation for #-2y#:
Equation 1:
#6x - 2y = 4#
#color(red)(-6x) + 6x - 2y = color(red)(-6x) + 4#
#0 - 2y = -6x + 4#
#-2y = -6x + 4#
Equation 2:
#-5x - 2y = 5#
#color(red)(5x) - 5x - 2y = color(red)(5x) + 5#
#0 - 2y = 5x + 5#
#-2y = 5x + 5#
Step 2) Because the left sides of both equations are equal we can now equate the right sides of both equations and solve for #x#:
#-6x + 4 = 5x + 5#
#color(red)(6x) - 6x + 4 - color(blue)(5) = color(red)(6x) + 5x + 5 - color(blue)(5)#
#0 - 1 = (color(red)(6) + 5)x + 0#
#-1 = 11x#
#-1/color(red)(11) = (11x)/color(red)(11)#
#-1/11 = (color(red)(cancel(color(black)(11)))x)/cancel(color(red)(11))#
#-1/11 = x#
#x = -1/11#
Step 3) Substitute #-1/11# for #x# into either equation in Step 1 and solve for #y#:
#-2y = -6x + 4# becomes:
#-2y = (-6 xx -1/11) + 4#
#-2y = 6/11 + 4#
#-2y = 6/11 + (11/11 xx 4)#
#-2y = 6/11 + 44/11#
#-2y = 50/11#
#color(red)(-1/2) xx -2y = color(red)(-1/2) xx 50/11#
#color(red)(2/2)y = color(red)(-1/color(black)(cancel(color(red)(2)))) xx (color(red)(cancel(color(black)(50)))25)/11#
#y = -25/11#
The Solution Is: #x = -1/11# and #y = -25/11# Or #(-1/11, -25/11)#
