How do you solve the following system?: #2x +y = 13 , 3x +2y = -2#

Question

Nathan Axel · Accepted Answer

#(x,y)=(28,-43)# Given: [1]#color(white)("XXX")2x+y=13# [2]#color(white)("XXX")3x+2y=-2# Multiply [1] by #2# to give #y# a coefficient equal to that in [2] [3]#color(white)("XXX")4x+2y=26# Subtract [2] from [3] to eliminate the #y# term [4]#color(white)("XXX")x=28# Substitute #28# for #x# back into [1] [5]#color(white)("XXX")2xx28 +y=13# Simplify [6]#color(white)("XXX")y=13-56 = -43#

Eva Adamson · Answer

#x=28#
#y=-43#

Given - #2x+y=13# ---------------------------(1) #3x+2y=-2# ---------------------------(2) Solve equation (1) for #y# #y=13-2x# Substitute #y=13-2x# in equation (2) #3x +2(13-2x)=-2# #3x+26-4x=-2# #-x+26=-2# #-x=-2-26# #-x=-28# #x=28# Substitute #x=28# in equation (1) #2(28)+y=13# #56+y=13# #y=13-56=-43# #y=-43#

Eva Adamson · Answer

undefined To solve the system of equations $2x + y = 13$ and $3x + 2y = -2$, follow these steps:

1. Use one of the equations to solve for one variable in terms of the other.
   
2. Substitute this expression into the other equation.

3. Solve for the variable.

4. Once you have found the value of one variable, substitute it back into one of the original equations to solve for the other variable.

5. The solution to the system will be the values of $x$ and $y$ that satisfy both equations simultaneously.