Step 1) Solve the first equation for #x#:
#0.5x + 4y = -1#
#0.5x + 4y - color(red)(4y) = -1 - color(red)(4y)#
#0.5x + 0 = -1 - 4y#
#color(red)(2) xx 0.5x = color(red)(2)(-1 - 4y)#
#1x = (color(red)(2) xx -1) - (color(red)(2) xx 4y)#
#x = -2 - 8y#
Step 2) Substitute #(-2 - 8y)# for #x# in the second equation and solve for #y#:
#x + 2.5y = 3.5# becomes:
#(-2 - 8y) + 2.5y = 3.5#
#-2 - 8y + 2.5y = 3.5#
#color(red)(2) - 2 - 8y + 2.5y = color(red)(2) + 3.5#
#0 - 8y + 2.5y = 5.5#
#-8y + 2.5y = 5.5#
#(-8 + 2.5)y = 5.5#
#-5.5y = 5.5#
#(-5.5y)/color(red)(-5.5) = 5.5/color(red)(-5.5)#
#(color(red)(cancel(color(black)(-5.5)))y)/cancel(color(red)(-5.5)) = -1#
#y = -1#
Step 3)* Substitute #-1# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:
#x = -2 - 8y# becomes:
#x = -2 - (8 * -1)#
#x = -2 - (-8)#
#x = -2 + 8#
#x = 6#
The Solution Is: #x = 6# and #y = -1# or #(6, -1)#
