Step 1) Solve each equation for #10x#:
Equation 1:
#-5x - 3y = 11#
#-5x - 3y + color(red)(3y) = 11 + color(red)(3y)#
#-5x - 0 = 11 + 3y#
#-5x = 11 + 3y#
#color(red)(-2) xx -5x = color(red)(-2)(11 + 3y)#
#10x = (color(red)(-2) xx 11) + (color(red)(-2) xx 3y)#
#10x = -22 + (-6y)#
#10x = -22 - 6y#
Equation 2:
#2x - 4y = 15#
#2x - 4y + color(red)(4y) = 15 + color(red)(4y)#
#2x - 0 = 15 + 4y#
#2x = 15 + 4y#
#color(red)(5) xx 2x = color(red)(5)(15 + 4y)#
#10x = (color(red)(5) xx 15) + (color(red)(5) xx 4y)#
#10x = 75 + 20y#
Step 2) Now that the left sides of both equations are equal, we can equate the right side of each equation and solve for #y#:
#-22 - 6y = 75 + 20y#
#-color(blue)(75) + -22 - 6y + color(red)(6y) = -color(blue)(75) + 75 + 20y + color(red)(6y)#
#-97 - 0 = 0 + (20 + color(red)(6))y#
#-97 = 26y#
#-97/color(red)(26) = (26y)/color(red)(26)#
#-97/26 = (color(red)(cancel(color(black)(26)))y)/cancel(color(red)(26))#
#-97/26 = y#
#y = -97/26#
Step 3) Substitute #-97/26# for #y# into the solution for either equation in Step 1 and calculate #x#:
#10x = -22 - 6y# becomes:
#10x = -22 - (6 xx -97/26)#
#10x = -22 - (-582/26)#
#10x = -22 + 582/26#
#10x = (26/26 xx -22) + 582/26#
#10x = -572/26 + 582/26#
#10x = 10/26#
#1/color(red)(10) xx 10x = 1/color(red)(10) xx 10/26#
#1/cancel(color(red)(10)) xx color(red)(cancel(color(black)(10)))x = 1/cancel(color(red)(10)) xx color(red)(cancel(color(black)(10)))/26#
#1x = 1/26#
#x = 1/26#
The Solution Is: #x = 1/26# and #y = -97/26# or #(1/26, -97/26)#
