Question

How do solve the following linear system?: `x-4y=-24 , x+y=-1`?

Answer 1

The lines cross at `(x,y)->(-28/5,+23/5)->(-5 3/5,+4 3/5)`

Explanation:

Given:
`color(white)(..)color(brown)(x-4y=-24)`......................(1)
`color(white)(..)color(brown)(x+y=-1)`..........................(2)
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Consider equation (2)

Take the `y` over to the other side of the = and change its sign

`x=-1-y`............................................(3)

Using equation (3) substitute for `x` in equation (1) giving

`x-4y=-24" becomes "-> -1-y-4y=-24`

Multiply everything by (-1) to change the signs

`1+y+4y=24`

`1+5y=24`

Move the left hand side 1 to the right and change its sign

`5y=24-1" = "23`

Divide both sides by 5 giving

`color(green)(y=23/5)`
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Substitute `y=23/5` in equation (2) giving:

`x+y=-1" becomes "->x+23/5=-1`

Move the `23/5` to the other side of = and change its sign

`x=-1-23/5 " = " -28/5`

`color(green)(x=-28/5)`
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So the lines cross at `(x,y)->(-28/5,23/5)->(-5 3/5,+4 3/5)`