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
