Question

How do you solve `4m+n=2` and `m-4n=9` using substitution?

Answer 1

`m=1" ; "n=-2`

Explanation:

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`