Question

How do you solve the system `3x-2y=2` and `5x-5y=10`?

Answer 1

The solution for the system of equation is
`color(red)(x = -2 , y=-4`

Explanation:

`3x-2y=2` ,multiplying the equation by `5`
`15x -color(red)( 10y) = 10`...........equation `1`

`5x-5y=10` , multiplying the equation by `2`
`10x - color(red)(10y) = 20`.......equation `2`

Subtracting equation `1` from `2` to eliminate `color(red)(10y`
`10x - cancelcolor(red)(10y) = 20`
`-15x +cancelcolor(red)( 10y) =- 10`

`-5x = 10`
`color(red)( x = -2`

Substituting `x` in equation `1` to find `y`
`3x - 2 = 2y`
`(3x-2)/2 =y`

`y = (3.(-2) - 2)/2`
`y = -8/2 = -4`
`color(red)(y=-4`