What is the solution to the system #x+y=2# and #x-y=6#? Algebra Systems of Equations and Inequalities Linear Systems with Addition or Subtraction 1 Answer David Drayer · EZ as pi Mar 6, 2018 #x = 4" and " y = -2 # Explanation: Add the two equations eliminating #y# to solve for #x# # " "x + y = 2 # # +x -y = 6# # 2x + 0y = 8 # # 2x = 8" " # divide each side by 2 # (2x)/2 = 8/2 # # x = 4 " "# Substitute 4 for x and solve for y # 4 + y = 2 " "# subtract 4 from each side # 4 -4 + y = 2 -4" " # This gives # y = -2 # Answer link Related questions What if the elimination method results in 0=0? How do you use the addition and subtraction method to solve a linear system? Can any system be solved using the addition and subtraction method? When is the addition and subtraction method easier to use? How do you solve #-x-6y=-18# and #x-6y=-6# using the addition and subtraction method? How do you solve #5x-3y=-14# and #x-3y=2# using elimination? Do you need to add or subtract the equations #5x+7y=-31# and #5x-9y=17# to solve the system? How do you solve the system of equations #3y-4x=-33# and #5x-3y=40.5#? What is the common point of #x+2y=6# and #x+y=2#? How do you use the addition and subtraction method to solve #4x+6y=16# and #3x-2y=-1#? See all questions in Linear Systems with Addition or Subtraction Impact of this question 6587 views around the world You can reuse this answer Creative Commons License