How do you solve the following system: #3x + 2y = 1, 2x - 3y = 10 #? Algebra Systems of Equations and Inequalities Systems Using Substitution 1 Answer G_Dub Apr 16, 2018 #x=23/13, y=-28/13# Explanation: #3x+2y=1# equation (1) #2x-3y=10# equation (2) From (2): #2x=3y+10 => x=(3y+10)/2# Substitute #x=(3y+10)/2# into (1); #3((3y+10)/2)+2y=1# #3(3y+10)+4y=2# #9y+30+4y=2# #13y=-28# #y=-28/13# Substitute #y=-28/13# into #x=(3y+10)/2#: #x=(3(-28/13)+10)/2=23/13# Answer link Related questions How do you solve systems of equations using the substitution method? How do you check your solutions to a systems of equations using the substitution method? When is the substitution method easier to use? How do you know if a solution is "no solution" or "infinite" when using the substitution method? How do you solve #y=-6x-3# and #y=3# using the substitution method? How do you solve #12y-3x=-1# and #x-4y=1# using the substitution method? Which method do you use to solve the system of equations #y=1/4x-14# and #y=19/8x+7#? What are the 2 numbers if the sum is 70 and they differ by 11? How do you solve #x+y=5# and #3x+y=15# using the substitution method? What is the point of intersection of the lines #x+2y=4# and #-x-3y=-7#? See all questions in Systems Using Substitution Impact of this question 1900 views around the world You can reuse this answer Creative Commons License