Question

How do you solve the system of equations: x - 2y = -1, 2x - y = 4?

Answer 1

The solutions are:
`color(blue)(x=3,y=2`

Explanation:

`x - 2y = -1` , multiplying this equation by `2`
`color(blue)(2x) -4y = -2` ....equation `(1)`

`color(blue)( 2x) - y = 4`.........equation `(2)`

Now we can solve through elimination as we have the term `color(blue)(2x)` common to both equations:

Subtracting equation `2` from `1`

`cancel(color(blue)(2x)) -4y = -2`
`-cancel(color(blue)( 2x)) + y =- 4`

`-3y=-6`
`color(blue)(y=2`

Now we find `x` by substituting `y` in equation `1`
`x - 2y = -1`
`x = -1+2y`
`x=-1+2*(2)`
`x=-1+4`
`color(blue)(x=3`