How do you solve the following system?: # -2x+3y=5, 3x+2y=12 # Algebra Systems of Equations and Inequalities Systems Using Substitution 1 Answer Barney V. Apr 2, 2017 #color(red)(y=3,x=2# Explanation: #:.-2x+3y=5#-----(1) #:.3x+2y=12#--------(2) #:.(2) xx 3# #:.9x+6y=36#--------(3) #:.(1) xx 2# #:.-4x+6y=10#------(4) #:.(3) -(4)# #:.13x=26# #:.color(red)(x=2# Substitute x=2 in (2) #:.3(2)+2y=12# #:.6+2y=12# #:.2y=12-6# #:.2y=6# #:.color(red)(y=3# Substitute # y=3,x=2# in (1) #:.-2(2)+3(3)=5# #:.-4+9=5# #:.color(red)(5=5# 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 4385 views around the world You can reuse this answer Creative Commons License