Given:
4m+n=24m+n=2 -------------------------------Equation (1)
m-4n=9m−4n=9..........................................Equation (2)
color(blue)("Determine the value of n")Determine the value of n
color(brown)("Showing every step in the first part to demonstrate method")Showing every step in the first part to demonstrate method
color(green)("Consider Equation (2)")Consider Equation (2)
color(green)("Add 4n to both sides")Add 4n to both sides
" "m-4n+4n=9+4n m−4n+4n=9+4n
color(green)("But "4n-4n=0)But 4n−4n=0
" "m=9+4n m=9+4n .....................................(3)
color(green)("Substitute for m in (1) using (3)")Substitute for m in (1) using (3)
" "4m+n=2" "->" "4(9+4n)+n=2 4m+n=2 → 4(9+4n)+n=2
color(green)("Multiply out the bracket")Multiply out the bracket
" "=>36+16n+n=2 ⇒36+16n+n=2
" "36+17n=2 36+17n=2
color(green)("Subtract 36 from both sides")Subtract 36 from both sides
" "17n=-34 17n=−34
color(green)("Divide both sides by 17")Divide both sides by 17
" "color(blue)(n=-34/17=-2) n=−3417=−2
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color(blue)("Determine the value of m")Determine the value of m
Substitute n=-2n=−2 into (2)
m-4n=9" "->" "m-4(-2)=9m−4n=9 → m−4(−2)=9
m+8=9m+8=9
m=9-8m=9−8
m=1m=1
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Check
4m+n=2" "->" "4(1)+(-2)=24m+n=2 → 4(1)+(−2)=2
m-4n=9" "->" "1-4(-2)=9m−4n=9 → 1−4(−2)=9
