Question

What is the solution to the following system of linear equations: `4x-y=-6` `x-2y=-5`?

Answer 1

`{(x=-1), (y=2) :}`

Explanation:

Your starting system of equations looks like this

`{(4x-y = -6), (x-2y = -5) :}`

Multiply the first equation by `(-2)` to get

`{(4x-y = -6 | * (-2)), (x-2y = -5) :}`

`{(-8x+2y = 12), (" "x-2y = -5) :}`

Notice that if you add the two equations by adding the left-hand sides and the right-hand sides separately, you can eliminate the `y`-term.

The resulting equation will have only one unknown, `x`.

`{(-8x+2y = 12), (" "x-2y = -5) :}`
`stackrel("-------------------------------------------")`

`-8x + color(red)(cancel(color(black)(2y))) + x - color(red)(cancel(color(black)(2y))) = 12 + (-5)`

`-7x = 7 implies x = 7/((-7)) = color(green)(-1)`

Plug this value of `x` into one of the two original equations to get the value of `y`

`4 * (-1) - y = -6`

`-4 - y = -6`

`-y = -2 implies y = ((-2))/((-1)) = color(green)(2)`

The solution set for this system of equations will thus be

`{(x=-1), (y=2) :}`