Step 1) Solve the second equation for #x#:
#x + 4y = -2#
#x + 4y - color(red)(4y) = -2 - color(red)(4y)#
#x + 0 = -2 - 4y#
#x = -2 - 4y#
Step 2) Substitute #(-2 - 4y)# for #x# in the first equation and solve for #y#:
#6x + 9y = 3# becomes:
#6(-2 - 4y) + 9y = 3#
#(6 xx -2) - (6 xx 4y) + 9y = 3#
#-12 - 24y + 9y = 3#
#-12 + (-24 + 9)y = 3#
#-12 + (-15)y = 3#
#-12 - 15y = 3#
#-12 + color(red)(12) - 15y = 3 + color(red)(12)#
#0 - 15y = 15#
#-15y = 15#
#(-15y)/color(red)(-15) = 15/color(red)(-15)#
#y = -1#
Step 3) Substitute #-1# for #y# in the solution to the second equation at the end of Step 1 and calculate #x#:
#x = -2 - 4y# becomes:
#x = -2 - (4 xx -1)#
#x = -2 - (-4)#
#x = -2 + 4#
#x = 2#
The Solution Is:
#x = 2# and #y = -1#
Or
#(2, -1)#
