Question

How do you complete the ordered pair (?, –4) given –2x + y = 3?

Answer 1

`(-7/2, -4)`

Explanation:

`-2 x + y = 3`

if `y = -4` then,
`-2 x + (-4) = 3`

add `4` to both sides,
#-2 x + (-4) + 4= 3 + 4

divide `-2` to bth sides
`(-2 x)/-2 = 7/-2`

`x = - 7/2`

Answer 2

`x=-7/2`

`P_1->(x,y)=(-7/2,-4)`

Explanation:

`color(blue)("Shortcut method")`

Substitute -4 for y

`-2x-4=3`

Make all positive negative and all positive negative

`+2x+4=-3`

Move the 4 to the other side of = and change its sign

`2x=-3-4=-7`

move the 2 from `2x` to the other side of = and change it from multiply to divide

`x=-7/2`

`color(brown)("With practice you should be able to do a lot of this in your head and write a lot less.")`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("First principle method")`
You are given a point on the line that I will call point 1 `->P_1`

`P_1->(x,y)=(x,-4)`

This point is on the strait line `"................ "-2x+y=3`

Substituting for y `color(green)(P_1->(x,color(red)(-4))" "->" "-2xcolor(red)(-4)=3)`

add 4 to both sides (gets rid of the -4 on the left)

but -4+4=0#

`-2x+0=3+4`

`-2x=7`

To make the `-2x` positive multiply both sides by -1

`+2x=-7`

Divide both sides by 2

`2/2 x=-7/2`

But `2/2=1 and 1xx x=x`

`x=-7/2`