Step 1) Solve the second equation for #y#:
#4x + y = 1#
#-color(red)(4x) + 4x + y = -color(red)(4x) + 1#
#0 + y = -4x + 1#
#y = -4x + 1#
Step 2) Substitute #(-4x + 1)# for #y# in the first equation and solve for #x#:
#6x + 2y = -2# becomes:
#6x + 2(-4x + 1) = -2#
#6x + (2 * -4x) + (2 * 1) = -2#
#6x + (-8x) + 2 = -2#
#6x - 8x + 2 = -2#
#(6 - 8)x + 2 = -2#
#-2x + 2 = -2#
#-2x + 2 - color(red)(2) = -2 - color(red)(2)#
#-2x + 0 = -4#
#-2x = -4#
#(-2x)/color(red)(-2) = (-4)/color(red)(-2)#
#(color(red)(cancel(color(black)(-2)))x)/cancel(color(red)(-2)) = 2#
#x = 2#
Step 3) Substitute #2# for #x# in the solution to the second equation at the end of Step 1 and calculate #y#:
#y = -4x + 1# becomes:
#y = (-4 * 2) + 1#
#y = -8 + 1#
#y = -7#
The solution is: #x = 2# and #y = -7# or #(2, -7)#
