Given:
#4m+n=2# -------------------------------Equation (1)
#m-4n=9#..........................................Equation (2)
#color(blue)("Determine the value of n")#
#color(brown)("Showing every step in the first part to demonstrate method")#
#color(green)("Consider Equation (2)")#
#color(green)("Add 4n to both sides")#
#" "m-4n+4n=9+4n#
#color(green)("But "4n-4n=0)#
#" "m=9+4n# .....................................(3)
#color(green)("Substitute for m in (1) using (3)")#
#" "4m+n=2" "->" "4(9+4n)+n=2#
#color(green)("Multiply out the bracket")#
#" "=>36+16n+n=2#
#" "36+17n=2#
#color(green)("Subtract 36 from both sides")#
#" "17n=-34#
#color(green)("Divide both sides by 17")#
#" "color(blue)(n=-34/17=-2)#
'.........................................................
#color(blue)("Determine the value of m")#
Substitute #n=-2# into (2)
#m-4n=9" "->" "m-4(-2)=9#
#m+8=9#
#m=9-8#
#m=1#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check
#4m+n=2" "->" "4(1)+(-2)=2#
#m-4n=9" "->" "1-4(-2)=9#
